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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
यदि `overset(rightarrow)(a)=hati-hatj-6hatk, overset(rightarrow)(b)=hati-hatj+4hatk` तथा `overset(rightarrow)(c)=2hati-5hatj+3hatk ` है तो `[overset(rightarrow)(a)overset(rightarrow)(b) overset(rightarrow)(c)]` का मान ज्ञात कीजिएः |
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Answer» आदिश त्रिगुण कि परिभाषा से `[overset(rightarrow)(a)overset(rightarrow)(b)overset(rightarrow)(c)]=|{:(,1,-1,-6),(,1,-1,4),(,2,-5,3):}|` `|{:(,0,0,-10),(,1,-1,4),(,2,-5,3):}| R_(1) to R_(1) to R_(2)` ltbr =30 |
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| 2. |
`[overset(rightarrow)(a) overset(rightarrow)(b)overset(rightarrow)(c)]` का मान ज्ञात कीजिएः यदि `overset(rightarrow)(a) =2hati+hatj-3hatk, overset(rightarrow)(b)=-hati+hatj+2hatk, overset(rightarrow)(c)=4hati+3hatk` |
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Answer» Correct Answer - 29 `[veca vecb vecc]=|{:(,a_(1),a_(2),a_(3)),(,b_(1),b_(2),b_(3)),(,c_(1),c_(2),c_(3)):}|` |
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| 3. |
`[overset(rightarrow)(a) overset(rightarrow)(b)overset(rightarrow)(c)]` का मान ज्ञात कीजिएः यदि `overset(rightarrow)(a) =hati+hatj+hatk, overset(rightarrow)(b)=hati-hatj+hatk, overset(rightarrow)(c)=hati+2hatj-hatk` |
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Answer» Correct Answer - 4 `[veca vecb vecc]=|{:(,a_(1),a_(2),a_(3)),(,b_(1),b_(2),b_(3)),(,c_(1),c_(2),c_(3)):}|` |
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| 4. |
`overset(rightarrow)(c).(overset(rightarrow)(a)xxoverset(rightarrow)(b))` का मान ज्ञात कीजिएः यदि `overset(rightarrow)(a)=5hati-4hatj+hatk, overset(rightarrow)(b)=-4hati+3hatj-2hatk, overset(rightarrow)(c)=hati-2hatj-7hatk` |
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Answer» `vecaxxvecb=|{:(,hati,hatj,hatk),(,5,-4,1),(,-4,3,2):}|=5hati+6hatj-hatk` अब `vecc.(vecaxxvecb)=(hati-2hatj-7hatk).(5hati+6hatj-hatk)` `=1.5+(-2)6+(-7)(-1)` |
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| 5. |
यदि a,b व c तीनो समतलिये सदिश नहीं है तब `axxb+bxxc+cxxa` व a+b+c का अदिश गुणन हैA. [a b c]B. 2[a,b,c]C. 3[a b c]D. इनमे से कोई नहीं |
| Answer» Correct Answer - C | |
| 6. |
यदि a,b व c समतलिये सदिश नहीं है तब `{:(,(i),a+b,b+c,c+a),(,(ii),a-b,b-c,c-a),(,(iii),axxb,bxxc,cxxa):}`A. [a,b,c]B. 2[a,b,c]C. 0D. [a,b,c] |
| Answer» Correct Answer - (i)B,(ii)C,(iii)D | |
| 7. |
a का वह मान जिसके लिए बिंदु सदिशों द्वारा `hati+ahatj+hatk, hatj+ahatk, ahati+hatk` बने सम्पषट्फलक का आयतन न्यूनतम होगा।A. `sqrt3`B. 2C. `(1)/(sqrt3)`D. 3 |
| Answer» Correct Answer - C | |
| 8. |
निम्न में से कोण-सा सदिश शेष तीनो सदिशों के बराबर नहीं हैA. `u.(vxxomega)`B. `(vxxomega).u`C. `v.(uxxomega)`D. `(u xx v).omega` |
| Answer» Correct Answer - C | |
| 9. |
एक इकाई सदिश `hati+hatj+2hatk` के समतल `hati+hatj+hatk` पर लम्ब है वह हैA. `(hati+hatj)/(sqrt2)`B. `(hati-hatj)/(sqrt2)`C. `pm(hatj-hatk)/(sqrt2)`D. इनमे से कोई नहीं |
| Answer» Correct Answer - C | |
| 10. |
यदि सदिश `vec(a)` समतल `vec(b)` `vec(c)` पर स्थित है तब निम्नलिखित में से कौन-सा विकल्प सही है?A. `[a b c] ne 0`B. `[a b c]=1`C. `a+b+c=0`D. `[b c a]=1` |
| Answer» Correct Answer - A | |
| 11. |
एक इकाई-सदिश `a=3hati+2hatj+6hatk` जो पर लम्ब व `b=2hati+hatj+hatk` तथा `c=hati-hatj+hatk` से समतलिये है वह है-A. `(6hati-5hatk)/(sqrt61)`B. `(3hati-hatk)/(sqrt10)`C. `(2hati-5hatj)/(sqrt29)`D. `(2hati+hatj-2hatk)/(3)` |
| Answer» Correct Answer - B | |
| 12. |
यदि a,b,c समतलिये सदिश नहीं है तब `(a+b+c).[(a+b)xx(axxc)]` बराबर है |
| Answer» Correct Answer - D | |
| 13. |
यदि `vec(a)=hati+hatj-hatk, vec(b)=hati-2hatj+hatk, vec(c)=hati-hatj-hatk` तब `vec(a)` व `vec(b)` के तल में वह सदिश जिसके `vec(c)` पर परपेक्ष का मापक `((1)/(sqrt3))` है होगा-A. `2hati-3hatj+2hatk`B. `4hati-7hatj+4hatk`C. `4hati-2hatj+2hatk`D. `4hati+3hatj-10hatk` |
| Answer» Correct Answer - D | |
| 14. |
यदि `ahatj+hatj+hatk, hati-bhatj+hatk, hati+hatj-chatk` व इकाई सदिश समतलिये है यदि, पर लम्ब है तब abc+2 बराबर हैA. a+b-cB. a-b-cC. a+b+cD. a-b+c |
| Answer» Correct Answer - B | |
| 15. |
यदि `a=2hati+hatj+hatk, b=hati+2hatj-hatk` व इकाई सदिश c समतलिये है यदि c,a पर लम्ब है तब c=A. `(1)/(sqrt2)(-hatj+hatk)`B. `(1)/(sqrt3)(-hati-hatj-hatk)`C. `(1)/(sqrt5)(hati-2hatj)`D. `(1)/(sqrt3)(hati-hatj-hatk)` |
| Answer» Correct Answer - A | |
| 16. |
यदि a,b,c समतलिये इकाई सदिश है तब आदिश त्रिगुण [2a-b 2b-c 2c-a]= |
| Answer» Correct Answer - A | |
| 17. |
माना `a=3hati-6hatj-hatk, b=hati+4hatj-3hatk` व `c=3hati-4hatj-12hatk` दिए गए सदिश है तब सदिश पर `axxb` का प्रक्षेपA. 14B. `-14`C. 12D. 15 |
| Answer» Correct Answer - B | |
| 18. |
यदि a.b=b.c=c.a=0 तब `a.(bxxc)` बराबर हैA. एक अशून्ये सदिशB. 1C. `-1`D. `|a||b||c|` |
| Answer» Correct Answer - D | |
| 19. |
यदि तीनो बिंदु A,B व C के स्थिति सदिश `hati+hatj, hati-hatk` व `phati+qhatj+rhatk` है तब, बिंदु समयरेखीये होंगे यदिA. p=q=r=1B. p=q=r=0C. p=q, r=0D. p=1, q=2, r=0 |
| Answer» Correct Answer - B,C,D | |
| 20. |
सिद्ध कीजिएः कि चारो बिंदु जिनके स्थिति सदिश `6hati-4hatj+10hatk, 5 hati-3hatj+10hatk, 4hati-6hati+10hatk, 2hatj+10hatk` एक संतलिये है |
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Answer» अदिश मान `1lambda,` के `mu` लिए रख सकते है `(6hati-4hatj+10hatk).1+lambda(5hati-3hatj+10hatk)+mu(4hati-6hatj+10hatk)+v(2hatj+10hatk)` `=0hati+0hatj+0hatk` अब दोनों और के गुणांकों की तुलना कीजिएः। |
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| 21. |
यदि `overset to a, oversetto b ,overset to c ` तीन सदिश हो तो सिद्ध कीजिए की ` [overset to a+oversetto boversetto b +overset to c overset to c +oversetto a ] =2 [ oversetto a overset to b overset to c ] ` |
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Answer» बाँया पक्ष `= [oversetto a + oversetto b oversetto b +overset to c oversetto c +overset to a ]` ` (oversetto a +overset to b )*[(oversetto b+overset to c )xx(oversetto c+oversetto a ) ]` ` " "=(overset to a+overset to b )*[overset to bxxoverset to c +overset to b xxoverset to a +overset to c xxoverset to c +overset to c xxoverset to a ]` ` =(overset to a +overset to b) *[overset to bxxoverset to c -overset to a xxoverset to b + 0+overset to c xxoverset to a ]` `" "(because overset to axxoverset tob =-overset to b xxoverset to a ("तथा") overset to c xxoverset to c =0) ` ` = (overset to a +overset to b )*[overset to bxxoverset to c -overset to a xxoverset to b+ overset to c xxoverset to a ]` ` =overset to a *(overset to b xxoverset to c ) -overset to a *(overset to a xxoverset to b ) +overset to a *(overset toc xxoverset to a )+ overset to b *(overset to b xxoverset to a ) ` `" "- oversettob *(oversetto axxoversettob )+ oversetto b*(oversetto c xxoversetto a ) ` ` = (oversetto a overset to b overset toc )-(overset toa overset toa overset tob) +(overset to aoverset to coverset to a )+ (overset to boverset to boverset toc ) - (overset to boverset to boverset to b ) +(overset to b overset tocoverset toa ) ` ` = (overset to aoverset to b overset toc ) -0+0+0-0+(overset to b overset to c overset toa ) ` ` [because (overset to aoverset to aoverset tob )= (overset toa overset tocoverset toa) =(overset to boverset tob overset toc)= (overset toboverset toaoverset tob)=0]` `=(oversetto aoversettob oversettoc) +(oversettoboversetto coversettoa ) ` ` = (oversettoaoversettoboversettoc)+(overset to aoversettob oversettoc) ` ` = 2(oversettoaoversettoboversettoc ) ` = दाँया पक्ष |
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| 22. |
यदि `oversetto a =hat i -hat j+ hat k ," " oversetto b =hat i -2hat j -hatk ` तथा `overset to c =3hati +phat j +5hat k ` समतलीय हो तो P का मान ज्ञात कीजिए| |
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Answer» तीन सनिदशों `oversetto a ,oversetto b ,oversetto c ` के एकसमतलीय होने के लिए प्रतिबंद ` rArr " "1(-10 +p) -(-1) (5+3) +1(p+6)=0 ` ` rArr " "-10 +p+8+p+6=0` `rArr " " 2p+4=0 " "rArr " " p =-2` |
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| 23. |
यदि `oversetto l,oversetto m,oversetto n` तथा `oversetto a,oversetto b,oversetto c` असमतलीय सदिश हो तो सिद्ध कीजिए की- |
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Answer» माना `vel=l_(1)hati+l_(2)hatj+l_(3)hatk, vecm=m_(1)hati+m_(2)hati+m_(3)hatk` `vecn=n_(1)hati+n_(2)hatj+n_(3)hatk, veca=a_(1)hati+a_(2)hatj+a_(3)hatk` `vecb=b_(1)hati+b_(2)hatj+b_(3)hatk, vecc=c_(1)hati+c_(2)hatj+c_(3)hatk` `[vecl vecm vecn]=|{:(,l_(1),l_(2),l_(3)),(,m_(1),m_(2),m_(3)),(,n_(1),n_(2),n_(3)):}|` `[vec axxvecb]=|{:(,hati,hatj,hatk),(,a_(1),a_(2),a_(3)),(,b_(1),b_(2),b_(3)):}|` `=[vecl vecm vecn] [veca xx vecb]=|{:(,l_(1),l_(2),l_(3)),(,m_(1),m_(2),m_(3)),(,n_(1),n_(2),n_(3)):}| |{:(,hati,hatj,hatk),(,a_(1),a_(2),a_(3)),(,b_(1),b_(2),b_(3)):}|` `=|{:(,l_(1)hati+l_(2)hatj+l_(3)hatk),(,m_(1)hati+m_(2)hatj+m_(3)hatk),(,n_(1)hati+n_(2)hatj+n_(3)hatk):}, {:(,l_(1)a_(1)+l_(2)a_(2)+l_(3)a_(3)),(,m_(1)a_(1)+m_(2)a_(2)+m_(3)a_(3)),(,n_(1)a_(1)+n_(2)a_(2)+n_(3)a_(3)):} , {:(,l_(1)b_(1)+l_(2)b_(2)+l_(3)b_(3)),(,m_(1)b_(1)+m_(2)b_(2)+m_(3)b_(3)),(,n_(1)b_(1)+n_(2)b_(2)+n_(3)b_(3)):}|` `|{:(,vecl,vecl.veca,vecl.vecb),(,vecm,vecm.veca,vecm.vecb),(,vecn,vecn.veca,vecn vecb):}| (therefore vecl .veca=vecl_(1)veca_(1)+vecl_(2)a_(2)+vecl_(3)a_(3))` `(C_(1) Leftrightarrow C_(3), C_(2) Leftrightarrow C_(1), C_(3) Leftrightarrow C_(2))` `|{:(,vecl.veca,vecl.vecb,vecl),(,vecm.veca,vecm.vecb,vecm),(,vecn.veca,vecn.vecab,vecn):}| ` यदि सिद्ध करना था |
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| 24. |
सिद्ध कीजिए की सदिश `oversetto a-2oversettob +3oversetto c,-2oversetto a +3oversetto b -4oversetto c ` तथा `oversetto a- 3oversettob+5oversettoc ` समतलीय है| |
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Answer» माना `oversetto u = oversetto a -2oversetto b +3oversetto c," " oversetto v =-2 oversetto a +3oversetto b -4oversetto c ` ` " " oversetto w =oversetto a -3oversetto b +5oversetto c ` तब `[vecu vecv vecw]=|{:(,1,-2,3),(,-2,3,-4),(,1,-3,5):}|` ` " "= 1 [15-12 ]-(-2) [-10+ 4] +3 [6-3]` ` " " =3-12 +9 12-12=0` `[overset to u , overset to v,overset to w ]=0 ` अतः ` oversetto u , oversetto v,oversetto w ` समतलीय है| |
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| 25. |
सिद्ध कीजिए की चार बिंदु जिनके सदिश `2hati +3hatj -hat k ` , hat i -2hat j +3hat k ,3hat i -2hat k ` तथा ` hat i -6hat j +6hat k ` है,एक समतलीय है| |
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Answer» माना दिए गए चार बिंदु `A,B,C` व D तथा O मूलबिंदु है| तथा `" "oversetto (OA) =2hat i +3hatj- hatk, " " oversetto (OB) =hat i -2hat j +3hatk ` `overset to (OC) =3hati + 4hatj -2hatk " " overset to (OD) =hati -6hatj+6hatk ` अब `oversetto (AB) =oversetto (OB) -oversetto (OA )=(hati -2hatj +3hatk )- (2hati +3hatj -hatk ) = -hati -5hatj +4hatk =oversetto u` माना ` oversetto (AC) =oversetto (OC) -oversetto (OA) =(3hati +4hatj -2hatk )- (2hati +3hatj - hatk )` `" "= -hati -9hatj+ 7hatk =oversetto w ` (माना ) हम जानते है की बिंदु `A,B,C,D` समतलीय होंगे यदि `oversetto u,oversetto v,oversetto w` समतलीय है| अतः `" "[ oversetto u, oversetto v, oversetto w]=|{:(,-1,-5,4),(,1,1,-1),(,-1,-9,7):}|` अब ` " "= -1 (-2) + 5 (6) +4 (-8) ` ` " "2+ 30-32 =0 ` अतः ` oversetto u,oversetto v,oversetto w ` अर्थात बिंदु `A,B,C,D` समतलीय है| |
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| 26. |
सिद्ध कीजिए की सदिश `hat i - 2hatj+ 3hat k ,-2hat i +3hat j -4hat k ` तथा `hat i -3hat j +5hat k ` एक समतलीय है| |
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Answer» माना `overset to a =hat i -2hat j +3hat k ` ` " "overset to b =-2hat i +3hat j -4hatk ` `Rightarrow |{:(,1,-1,1),(,1,-2,-1),(,3,p,5):}|` तथा `" "overset to c =hat i -3hat j +5hat k ` उपरोक्त तीनो सदिशों के एकसमतलीय होने के लिए आवश्यक प्रतिबंद `[overset to a overset tob overset to c ] =0 ` `|{:(,1,-2,3),(,-2,3,-4),(,1,-3,5):}|` इसलिए ` " "= 1 (15-12)-(-2) (-10+4) +3(6-3) ` ` " "= 3+2(-6) +3(3) ` ` " "= 3-12+9=0 ` `rArr "[ oversetto aoversetto b oversetto c ]=0 ` `rArr` सदिश `oversetto a ,oversetto b, oversetto c ` एक समतलीय होंगें| |
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| 27. |
सिद्ध कीजिए की चार बिंदु ` A,B,C `और D जिनके निर्देशांक क्रमशः `(4,5,1),(0,-1,-1) ,(3,9,4) ` और `(-4,4,4)` है,एक समतलीय है| |
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Answer» माना O मूलबिंदु है,तब ` oversetto (OA) =4hati +5hat j+ hat k ` `oversetto (OB) =0hat(i) -hat j- hat k ` ` oversetto (OC) =3hati +9hat j +4hatk ` ` oversetto (OD) =-4hati +4hatj +4hatk ` अब ` oversetto (AB) =oversetto (OB) -oversetto (OA) =(0hat i -hatj- hat k )- (4hati + 5hat j +hatk ) ` ` " "= -4hat i -6hatj - 2hatk =oversetto u ` (माना) ` oversetto (AC) =oversetto (OC) -oversetto (OA) =(3hati +9hat j +4hatk )- (4hati + 5hat j +hatk )` `" " =-hati+ 4hatj +3hatk =oversetto v ` (माना) बिंदु A,B,C,D एक समतलीय होंगें यदि सदिश ` oversetto (AD)= oversetto (OD) - oversetto (OA) =(-4hati +4hatj +4hatk )- (4hat i + 5hatj +hat k ) ` ` " "=- 8hati -hatj +3hatk = oversetto w` (माना) बिंदु A,B,C,D एक समतलीय होंगें यदि सदिश `oversetto (AB),oversetto (AC) "तथा" oversetto (AD) "अर्थात" oversetto u,oversetto v` तथा `oversetto w` एक समतलीय होंगें| अतः ` " "[ oversetto uoversetto voversetto w] =0` अब `=|{:(,-4,-6,-2),(,-1,4,3),(,-8,-1,3):}|` ` " "=- 4(12+3) +6(-3+24) -2(1+32) ` ` " " =-60+126-66=0` अतः बिंदु `A,B,C,D` एक समतलीय है| |
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| 28. |
`lambda ` का मान ज्ञात कीजिए यदि सदिश `2hati -hatj +hatk ,hati+2hatj -hatk ` तथा ` 3hati +lambdahatj +5hatk ` एक समतलीय है| |
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Answer» माना `oversetto A=2hati -hatj +hatk ` ` oversetto B =hati +2hatj -hatk ` `oversetto C =3hati +lambda hatj +5hatk ` सदिश `oversetto A,oversetto B,oversetto C` एक समतलीय होंगे यदि `[oversetto Aoversetto B oversetto C ]=0` अब `[vecA vec B vecC]=|{:(2,-1,1),(1,2,-1),(3,lambda,5):}|=0` ` rArr " " 2(10 +lambda )+ 1(5+3) + 1(lambda -6 )=0 ` ` " "20 + 2lambda +8+lambda -6=0` ` " "3lambda +22=0` ` " "lalmbda =-(22)/(3)` |
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| 29. |
सिद्ध कीजिए कि `hati xx(oversettoaxxhati )+hatj xx(oversettoa xxhatj )+hatk xx(oversettoa xxhatk ) =2oversettoa ` |
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Answer» हम जानते है कि ` oversetto axx( oversetto b xx oversetto c)=( oversetto a * oversetto c) oversetto b -( oversetto a* oversetto b ) oversetto c` `therefore hati xx(oversetto axxhati ) =(hati *hati )oversetto a -(hati*oversetto a ) hati =oversetto a -(hati*oversetto a ) hati " "...(1)` ` " "(because hati *hati =1) ` इसी प्रकार `hati xx(oversetto a xxhatj )= oversetto a -(hatj *oversetto a ) hatj " "...(2)` तथा ` " "hatk xx(oversetto axxhatk) =oversetto a -(hatk *a ) hatk " "...(3) ` समीकरण (1 ) ,(2 ) व (3 ) को जोड़ने पर ` hati xx(oversetto a xxhati )+hatj xx(oversetto a xxhatj )+hatk xx(oversetto axxhatk }...(4)` माना ` oversetto a =lhati +mhatj +nhatk " "...(5)` तब ` hati *oversetto a =hati *(lhati+mhatj +nhatk ) ` ` " "= l (hati *hati ) + m (hati *hatj )+n(hati *hatk ) ` ` " "= l(1) +m (0) +n(0) =1` इसी प्रकार `hatj *oversetto a= m ` तथा `hatk *oversetto a =n ` अतः समीकरण (5 ) से ` oversetto a = (hati *oversettoa )hati +(hatj *oversettoa ) hatj +(hatk *oversettoa ) hatk " "...(6) ` समीकरण (6 ) का प्रयोग समीकरण (4 ) में करने पर ` hati xx(oversetto axxhati )+hatj xx(oversetto a xxhatj )+ hatk xx(oversetto a xxhatk ) =3oversetto a -oversetto a =2oversetto a ` |
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| 30. |
यदि `oversetto a=3hati + 2hatj +2hatk ,oversetto b =-hati +3hatj +hatk ` तथा `oversetto c =hati+hatj +hatk ` तो `oversetto axx(oversetto b xxoversetto c ) ` का मान ज्ञात कीजिए| |
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Answer» हम जानते है की ` " "oversetto axx(oversetto bxxoversetto c) =(oversetto a *oversetto c)oversetto b -(oversetto a *oversetto b )oversetto c " "...(1)` अब ` oversetto a*oversetto c=(3hati +2hatj +2hatk )*(hati +hatj +hatk )` ` " "= 3xx1+2xx1+2xx1=3+2+2=7` ` oversetto a*oversetto b =(3hati +2hatj +2hatk )*(-hati +3hatj -hatk ) ` ` " " =3 (-1) +2(3)+2(-1)=-3+6-2=1` ये सभी मान समीकरण (1 )में रखने पर `oversetto a xx(oversetto bxxoversetto c) =7oversetto b -1oversetto c=7(-hati +3hatj-hatk)- (hati +hatj+hatk ) ` ` " "7hati+21hatj-7hatk-hati -hatj-hatk ` ` " "=-8hati+20hatj -8hatk` |
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| 31. |
शीर्षबिंदु A(1,-1,10), B(-1,-3,7), `C(5,-1, lambda)`,D(7,-4,7) वले चतुष्फलक का आयतन 11 घन इकाई है तब का `lambda` मान ज्ञात कीजिएः।A. `-1`B. 1C. `7`D. 7 |
| Answer» Correct Answer - B,D | |
| 32. |
उस समांतर षट्फलक का आयतन ज्ञात कीजिए जिसकी भुजाएं निम्न सदिशों द्वारा प्रदर्शित कि गयी है| ` oversetto a = 2hati -3hatj + hatk ,oversetto b =hati -hatj +2hatk `व `oversetto c =2hati +hatj -hatk ` |
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Answer» दिया है `oversetto a =2hati -3hatj +hatk ,oversetto b =hati -hatj+ 2hatk ` व `oversetto c =2hati +hatj -hatk ` तब `[vec a vecb vecc]=|{:(,2,-3,1),(,1,-1,2),(,2,1,-1):}|` `=2(1-2)+3(-1-4)+1(1+2)` `=-2-15+3=-14` अतः समांतर षट्फलक का आयतन ` |[ oversetto a oversetto b oversetto c ]| =|-14|` घन इकाई |
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| 33. |
समान्तर पष्टफल का आयतन जिसकी दी भुजाओ है | `vecOA = 2 hati- 3hatj , vecOB = hati + hatj - hatk , vecOC - 3hati - hatk `-A. `4//13`B. 14C. `2//7`D. इनमे से कोई नहीं |
| Answer» Correct Answer - B | |
| 34. |
समान्तर पष्टफल का आयतन 546 है जिसकी भुजाओ `-12hati+lambdahatk+3hatj-hatk, 2hati+hatj-15hatk` है तब `lambda` का मान हैA. 2B. 1C. `-3`D. 0 |
| Answer» Correct Answer - C | |
| 35. |
उस समान्तर पस्थ्फल का आयतन ज्ञात कीजिएः जिसकी सतत भुजाओ निम्न सदिशों द्वारा प्रदर्शित कि गयी है `vec(a)=hati+hatj, hatk, vec(b)=hati-hatj+hatk, vec(c)=hati+2hatj-hatk` |
| Answer» Correct Answer - 4 घन इकाई | |
| 36. |
`lambda` का वह मान ज्ञात कीजिएः जिसकी लिए `vec(a),vec(b),vec(c)` संतलिये है यहाँ `vec(a)=2hati-hatj+hatk, vec(b)=hati+2hatj+3hatk` व `vec(c)=3hati+lambdahatj+5hatk` |
| Answer» Correct Answer - `lambda=2 | |
| 37. |
मान ज्ञात कीजिएः `(2hati-3hatj).{(hati+hatj-hatk)xx(3hati-hatk)}` |
| Answer» Correct Answer - 4 | |
| 38. |
`lambda` का मान ज्ञात कीजिएः यदि सदिश `hati-hatj+hatk, 3hati+hatkj+2hatk` तथा `hati+lambdahatj-3hatk` समतलिये है |
| Answer» Correct Answer - `lambda=15` | |
| 39. |
`[vec(a) vec(b) vec(c)]` का मान ज्ञात कीजिएः यदि `vec(a)=hati-2hatj+3hatk, vec(b)=2hati-3hatj+hatk` तथा `vec(c)=3hatj+hatj+2hatk` है |
| Answer» Correct Answer - 28 | |
| 40. |
x का मान ज्ञात कीजिएः यदि बिंदु A(3,2,1), B(4,x,5),C(4,2,-2) एव (6,5,-1) समतलिये है |
| Answer» Correct Answer - x=5 | |
| 41. |
`lambda` का मान ज्ञात कीजिएः यदि सदिश `vec(a)=hati+3hatj+hatk, vec(b)=2hati-hatj-hatk` एव `vec(c)=lambdahati+7hatj+3hatk` समतलिये है |
| Answer» Correct Answer - `lambda=0` | |