If the angles between the vectors `veca` and `vecb,vecb` and `vecc,vecc` an `veca` are respectively `pi/6,pi/4` and `pi/3`, then the angle the vector `veca` makes with the plane containing `vecb`and `vecc`, isA. `cos^(-1)sqrt(1-sqrt(2//3))`B. `cos^(-1)sqrt(2-sqrt(3//2))`C. `cos^(-1)sqrt(sqrt(3//2)-1)`D. `cos^(-1)sqrt(sqrt(2//3))`

If the angles between the vectors `veca` and `vecb,vecb` and `vecc,vec

1.	If the angles between the vectors `veca` and `vecb,vecb` and `vecc,vecc` an `veca` are respectively `pi/6,pi/4` and `pi/3`, then the angle the vector `veca` makes with the plane containing `vecb`and `vecc`, isA. `cos^(-1)sqrt(1-sqrt(2//3))`B. `cos^(-1)sqrt(2-sqrt(3//2))`C. `cos^(-1)sqrt(sqrt(3//2)-1)`D. `cos^(-1)sqrt(sqrt(2//3))`
Answer» Correct Answer - B Let `theta` be angle between `veca` and plane containing `vecb` and `vecc`. `therefore 90^(@)-theta`= angle b/w `veca` and `vecb xx vecc` `\|hata xx (hatb xx hatc)\|^(2)=\|(hata.hatc)hatb-(hata.hatb)hatc\|^(2)` `=sin^(2)(90^(@)-theta)sin^(2)pi/4 = \|(cospi/3)hatb-(cospi/6)hatc\|^(2)` `rArr cos^(2)theta xx 1/2 =1/4 +3/4-2 xx 1/2 xx sqrt(3)/2 xx 1/sqrt(2)` `=1-sqrt(3)/2sqrt(2)` `rArr cos^(2)theta=2-sqrt(3//2)`

Discussion

No Comment Found

Related InterviewSolutions

The volume of the parallelepiped whose coterminous edges are represented by the vectors `2vecb xx vecc, 3vecc xx veca` and `4veca xx vecb` where `veca=(1+sintheta)hati+costhetahatj+sin2thetahatk` , `vecb=sin(theta+(2pi)/(3))hati+cos(theta+(2pi)/(3))hatj+sin(2theta+(4pi)/(3))hatk`, `vecc=sin(theta-(2pi)/(3))hati+cos(theta-(2pi)/(3))hatj + sin(2theta-(4pi)/(3))hatk` is 18 cubic units, then the values of `theta`, in the interval `(0,pi/2)`, is/areA. `pi/9`B. `(2pi)/(9)`C. `pi/3`D. `(4pi)/9`
Let `(hatp xx vecq) xx (hatp.vecq)vecq` `=(x^(2)+y^(2))vecq + (14-4x-6y)vecp` Where `hatp` and `hatq` are two non-collinear vectors `vecp` is unit vector and x,y are scalars. Then the value of `(x+y)` isA. 4B. 5C. 6D. 7
If `veca, vecb, vecc` are non coplanar vectors and `vecp, vecq, vecr` are reciprocal vectors, then `(lveca+mvecb+nvecc).(lvecp+mvecq+nvecr)` is equal toA. `l^(2)+m^(2)+n^(2)`B. lm+mn+nlC. 0D. None of these
If `veca, vecb, vecc` are three non-zero vectors, then which of the following statement(s) is/are true?A. `veca xx (vecb xx vecc), vecb xx (vecc xx veca), (vecc xx veca), vecc xx (veca xx vecb)` form a right handed systemB. `vecc, (veca xx vecb) xx vecc, veca xx vecb` from a right handed systemC. `veca.vecb+vecb.vecc+vecc.veca lt 0` if `veca+vecb+vecc=vec0`D. `((veca xx vecb).(vecb xx vecc))/((vecb xx vec).(veca xx vecc))=-1` if `veca + vecb + vecc=0`
Vectors `veca, vecb, vecc` are three unit vectors and `vecc` is equally inclined to both `veca` and `vecb`. Let `veca xx (vecb xx vecc) + vecb xx (vecc xx veca)` `=(4+x^(2))vecb-(4xcos^(2)theta)veca`, then `veca` and `vecb` are non-collinear vectors, `x gt 0`A. `x=2`B. `theta=0^(@)`C. `theta=x`D. `x=4`
`veca=2veci+vecj+veck`, `vecb=b_(1)hati+b_(2)hatj+b_(3)hatk`, `veca xx vecb=5hati+2hatj-12hatk, veca.vecb=11`, then `b_(1)+b_(2)+b_(3)=`A. 3B. 5C. 7D. 9
If `veca` and `vecb` are unequal unit vectors such that `(veca -vecb) xx [(vecb+veca) xx (2veca+vecb)]=veca+vecb`, then angle `theta` between `veca` and `vecb` can beA. `pi/2`B. 0C. `pi`D. `pi/4`
if `veca=hati+hatj+2hatk, vecb=hati+2hatj+2hatk` and `|vecc|=1` Such that `[veca xx vecb vecb xx vecc vecc xx veca]` has maximum value, then the value of `|(veca xx vecb) xx vecc|^(2)` is
`veca=2hati+hatj+2hatk, vecb=hati-hatj+hatk` and non zero vector `vecc` are such that `(veca xx vecb) xx vecc = veca xx (vecb xx vecc)`. Then vector `vecc` may be given asA. `4hati+2hatj+4hatk`B. `4hati-2hatj+4hatk`C. `hati+hatj+hatk`D. `hati-4hatj+hatk`
If the angles between the vectors `veca` and `vecb,vecb` and `vecc,vecc` an `veca` are respectively `pi/6,pi/4` and `pi/3`, then the angle the vector `veca` makes with the plane containing `vecb`and `vecc`, isA. `cos^(-1)sqrt(1-sqrt(2//3))`B. `cos^(-1)sqrt(2-sqrt(3//2))`C. `cos^(-1)sqrt(sqrt(3//2)-1)`D. `cos^(-1)sqrt(sqrt(2//3))`

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment