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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. |
If the points `(1,1,p)` and `(-3,0,1)` be equidistant from the plane `vecr.(3hati+4hatj-12hatk)+13`, find the values of p.A. `-1,(-7)/(3)`B. `1,(-7)/(3)`C. `-1,(7)/(3)`D. `1,(7)/(3)` |
| Answer» Correct Answer - D | |
| 2. |
Find the equation of a plane containing the line of intersectionof the planes `x+y+z-6=0a n d2x+3y+4z+5=0`passing through `(1,1,1)`.A. `10x+13y+16z+39=0`B. `10x-13y+16z+39=0`C. `10x+13y-16z+39=0`D. `10x+13y-16z-39=0` |
| Answer» Correct Answer - D | |
| 3. |
The equation of the plane passing through the points (0,1,2) and (-1,0,3) and perpendicular to the plane `2x+3y+z=5` isA. `3x -4y + 18z+32 =0`B. `3x +4y -18z + 32 =0`C. `4x + 3y -17z + 31 =0`D. `4x -3y + z + 1 =0` |
| Answer» Correct Answer - D | |
| 4. |
Find the vector equation of the plane which is at a distance of 5 units from the origin and which is normal to the vector `2hati + hatj + 2hatk`.A. `barr.(2hati+hatj+2hatk)=3`B. `barr.(2hati+hatj+2hatk)=5`C. `barr.(2hati+hatj+2hatk)=15`D. `barr.(2hati+hatj+2hatk)=45` |
| Answer» Correct Answer - C | |
| 5. |
The vector equation of the plane passing through the points `(1,-2,1),(2,-1,-3) and (0,1,5)` isA. `barr.(hati-4hatk)=5`B. `barr.(hati+4hatk)=5`C. `barr.(hati-4hatk)=5`D. `barr.(hati+4hatk)=5` |
| Answer» Correct Answer - D | |
| 6. |
The equation of plane passing through point (3 ,4 ,5) and parallel to the vectors `hati+2hatj+3hatk and 3hati+2hatj+4hatk` isA. `x+5y-4z+6=0`B. `2x+5y-4z-6=0`C. `2x -5y +z -6 =0`D. `2x+y+4z-7=0` |
| Answer» Correct Answer - B | |
| 7. |
The equation of plane in vector form passing through the points `(1 ,0 ,1 ) ,(1 , -1 , 1) and (4 , -3 ,2 )` isA. `barr.(hati-3hatk)=2`B. `barr.(-hati+3hatk)=2`C. `barr.(hati-3hatk)=4`D. `barr.(-hati+3hatk)=4` |
| Answer» Correct Answer - B | |
| 8. |
Find the vector equation of the plane passing through the point having position vector `2hati + 3hatj + 4hatk` and perpendicular to the vector `2hati + hatj -2hatk`.A. `barr.(2hati+hatj-2hatk)=-1`B. `barr.(2hati+hatj-2hatk)=8`C. `barr.(2hati+hatj-2hatk)=9`D. `barr.(2hati+hatj-2hatk)=15` |
| Answer» Correct Answer - A | |
| 9. |
Find the equation of theplane passing through the line `(x-1)/5=(y+2)/6=(z-3)/4`and point `(4,3,7)dot`A. `4x+8y+7z=41`B. `4x-8y+7z=41`C. `4x-8y-7z=41`D. `4x-8y+7z=39` |
| Answer» Correct Answer - B | |
| 10. |
The cartesian equation of the plane passing through the points `(1 ,1,2),(0,2,3) and(4,5,6)` isA. `y-z+1=0`B. `y+z-1=0`C. `y-z-1=0`D. `y+z+1=0` |
| Answer» Correct Answer - A | |
| 11. |
Find the vector and cartesian equations of the plane that passes through the point `(0, 1, -2)` and normal to the plane is `hti + hatj + hatk`.A. `x + y + z = 1`B. `x + y + z =-1`C. `x + y+ z = -2`D. `x + y + z = 3` |
| Answer» Correct Answer - B | |
| 12. |
Find the vector equation of the plane which is at a distance of 6 units from the origin and which is normal to the vector `2hati - hatj + 2hatk`.A. `barr.(2hati-hatj+2hatk)=3`B. `barr.(2hati-hatj+2hatk)=6`C. `barr.(2hati-hatj+2hatk)=9`D. `barr.(2hati-hatj+2hatk)=18` |
| Answer» Correct Answer - D | |
| 13. |
The line `vec r = veca+lambda vec b` will not meet the plane `vecr. vecn= vecq`, if___A. `vecb. vecn=0, veca. vecn=q`B. `vecb.vecn ne 0, veca.vecn ne q`C. `vecb.vecn = 0, veca.vecn ne q`D. `vecb.vecn ne 0, veca.vecn = q` |
| Answer» Correct Answer - C | |
| 14. |
The distance of the point P from the plane p from the plane p is __A. 1B. `(1)/(sqrt3)`C. `sqrt3`D. `(sqrt3)/(2)` |
| Answer» Correct Answer - B | |
| 15. |
A unit vector parallel to the intersection of planes `vecr.( hati- hatj + hat k)=5 and vec r .(2 hati+ hatj-3 hatk)=4` is ___A. `(2 hati+5 hatj-3 hatk )/(sqrt38)`B. `(2 hati-5 hatj+3 hatk )/(sqrt38)`C. `(2 hati+5 hatj+3 hatk )/(sqrt38)`D. `(-2 hati+5 hatj-3 hatk )/(sqrt38)` |
| Answer» Correct Answer - C | |
| 16. |
State which of the following statement is true ?A. The plane through the points A,B, C whose coordinates are `(1,1,1,), (-1,-3,-5)` respectively, passes though the point `(2, k, 4)` for all values of k.B. The equation of the plane which is parallel to the points `vecr .(2 hati-3 hatj+5 hatk)+7=0`C. The equation of the line of intersection of plane `3x+y+z=6 and x-y+2z=5` `(4x-11)/(3)=(4y+9)/(5)=(z-0)/(1)`D. The equation of a straight line `(x+3)/(2)=(y-4)/(3)=(z+5)/(2)` and the plane `4x-2y-z=1` are prependicular to each other |
| Answer» Correct Answer - A | |
| 17. |
Let `P_(1)` denotes the equation of the plane to which the vector `( hati+ hatj)` is normal and which constains the line (L) whose equation is `vecr =hati+ hatj+ hatk+ lambda( hati- hatj- hatk)` and `P_(2)` denotes the equation of the plane containing the line L and a pouint with position of the ` hatj ` which of the following holds good?A. The equation `P_(1) is x+y=2`B. The equation `P_(2) is vecr .( hati-2n hatj+ hatk)=2`C. The acute angle between `P_(1) and P_(2) is cost ^(1) sqrt3`D. The angle between the pl,ane `P_(2)` and the line (L) is ` tan^(-1 sqrt3` |
| Answer» Correct Answer - A::C | |
| 18. |
A plane meets the coordinates axes in A, B, C such that the centroid of the triangle ABC is the point (a,a,a) .Then the equation of the plane is `x+y+z=p`, where p is ___A. `6a`B. `-3a`C. 0D. `3a` |
| Answer» Correct Answer - D | |
| 19. |
If a variable plane which is at a constant distance 3p from the origin cut the co-ordinate axes at points A ,B , C , then locus of the centroid of `DeltaABC` isA. `(1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(9p^(2))`B. `(1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(3p^(2))`C. `(1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(p^(2))`D. `(1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(3)/(p^(2))` |
| Answer» Correct Answer - C | |
| 20. |
If a plane meets the co-ordinate axes in A ,B , C such that the centroid of triangle ABC is (p ,q , r) then the equation of plane isA. `(x)/(p)+(y)/(q)+(z)/(r)=3`B. `(x)/(p)+(y)/(q)+(z)/(r)=1`C. `(x)/(p)+(y)/(q)+(z)/(r)=0`D. `(x)/(p)+(y)/(q)+(z)/(r)=2` |
| Answer» Correct Answer - A | |
| 21. |
The angle at which the normal vector to the plane `4x+8y+z=5` inclined to the Z-axis isA. `"cos"^(-1)((8)/(9))`B. `"cos"^(-1)((1)/(9))`C. `"cos"^(-1)((2)/(9))`D. `"cos"^(-1)((4)/(9))` |
| Answer» Correct Answer - B | |
| 22. |
If plane meets co-ordinates axes at A , B ,C such that centroid of triangle ABC is `((1)/(3),(2)/(3),(4)/(3))` ,then the equation of plane isA. `x+2y+4z=4`B. `4x+2y+z=4`C. `x+y+z=4`D. `x+2y+3z=8` |
| Answer» Correct Answer - B | |
| 23. |
The equation of a plane which cuts equal intercepts of unit length on the axes isA. `x+y+z=0`B. `x+y+z=1`C. `x+y-z=1`D. `x+y+z=a` |
| Answer» Correct Answer - B | |
| 24. |
Find the angles at which the normal vector to tehplane `4x+8y+z=5`is inclined to the coordinate axes.A. `"cos"^(-1)((8)/(9))`B. `"cos"^(-1)((1)/(9))`C. `"cos"^(-1)((2)/(9))`D. `"cos"^(-1)((4)/(9))` |
| Answer» Correct Answer - D | |
| 25. |
IF for a plane the intercepts on the coordinate axes are 8,4,4 then the length of the perpendicular from the origin on to the plane is (A) `8/3` (B) `3/8` (C) `3` (D) `4/3`A. `(8)/(3)`B. `(3)/(8)`C. `(4)/(3)`D. `(3)/(4)` |
| Answer» Correct Answer - A | |
| 26. |
XOZ-plane divides the join of (2,3,1) and (6,7,1) in the ratioa. 3:7 b. 2:7c. -3:7 d. -2:7A. `3 : 7`B. `-2 :7`C. `-3 :7`D. `7 : 3` |
| Answer» Correct Answer - C | |
| 27. |
The lines `(x-2)/(1)=(y-3)/(1)=(z-4)/(-k) and (x-1)/(k)=(y-4)/(2)=(z-5)/(1)` are coplanar if __A. `k=1 or -1`B. `k-0 or -3`C. `k=3 or -3`D. `k=0 or -1` |
| Answer» Correct Answer - B | |
| 28. |
The angle between the line `(x-1)/(2)=(y-2)/(1)=(z+3)/(-1)` and the plane `x+y+4=0` is __A. `45^(@)`B. `60^(@)`C. `30^(@)`D. `75^(@)` |
| Answer» Correct Answer - B | |
| 29. |
The distance between the parallel planes `x+2y-2z-1=0 and 2x+4y-4z+5=0` is __A. 1 unitB. `(6)/(7)` unitsC. `(7)/(6)` unitsD. `(5)/(7)` units |
| Answer» Correct Answer - C | |
| 30. |
The point in which the line `(x-2)/(3)=(y+1)/(4)=(z-2)/(12)` meets the plane `x-2y+z=20` is __A. `(8,7,26)`B. `(-8,7,26)`C. `(8,-7,26)`D. `(8,7,-26)` |
| Answer» Correct Answer - A | |
| 31. |
If the planes `x-cy-bz=0, cx-y+az=0 and bx+ay-z=0` pass through a line, then the value of `a^2+b^2+c^2+2abc` is…. |
| Answer» Correct Answer - C | |
| 32. |
The planes `bx-ay=n,cy-bz=l,az-cx=m` intersect in a line if___A. `al+bm+cn=1`B. `al-bm-cn=0`C. `al+bm+cn=0`D. none of these |
| Answer» Correct Answer - C | |
| 33. |
The equation of the plane passing through the point (-1, 2, 1) and perpendicular to the line joining the points (-3, 1, 2) and (2, 3, 4) is · · · · · ·A. `barr.(5hati+2hatj+2hatk)=-5`B. `barr.(5hati+2hatj+2hatk)=4`C. `barr.(5hati+2hatj+2hatk)=1`D. `barr.(5hati+2hatj+2hatk)=2` |
| Answer» Correct Answer - C | |
| 34. |
Find the vector and Cartesian equation of the plane that passes throgh the point (1,0,-2) and the normal vector to the plane is `hati+hatj-hatk.`A. `barr.(hati+hatj+hatk)=-1`B. `barr.(hati+hatj+hatk)=1`C. `barr.(hati+hatj+hatk)=-2`D. `barr.(hati+hatj+hatk)=2` |
| Answer» Correct Answer - A | |
| 35. |
Find the vector equation of the plane passing through a point having position vector `3hati - 2hatj + 3hatk` and perpendicular to the vector `4hati + 3hatj + 2hatk`.A. `barr.(4hati+3hatj+2hatk)=12`B. `barr.(4hati+3hatj+2hatk)=16`C. `barr.(4hati+3hatj+2hatk)=8`D. `barr.(4hati+3hatj+2hatk)=20` |
| Answer» Correct Answer - C | |
| 36. |
The vector equation of the plane passing through the points `(1 ,1 2) ,(0 , 2 ,3) and (4 , 5 ,6)` isA. `barr.(7hatj+7hatk)=-7`B. `barr.(7hatj+7hatk)=7`C. `barr.(7hatj-7hatk)=-7`D. `barr.(7hatj-7hatk)=7` |
| Answer» Correct Answer - C | |
| 37. |
The cartesian form of the equation of plane `barr=(s+t)hati+(2+t)hatj+(3s+2t)hatk` isA. `3x +y +z = -2`B. `3x + y + z =2`C. `3x -y-z=-2`D. `3x-y -z =2` |
| Answer» Correct Answer - C | |
| 38. |
Find the vector equation of the plane passing through the point `hati + hatj -2hatk` and `hati + 2hatj + hatk, 2hati - hatj + hatk.`A. `barr.(9hati+3hatj-hatk)=4`B. `barr.(9hati+3hatj-hatk)=8`C. `barr.(9hati+3hatk-hatk)=14`D. `barr.(9hati+3hatk-hatk)=16` |
| Answer» Correct Answer - C | |
| 39. |
Find the cartesian form of the equation of the plane. `barr = (hati + hatj) + s(hati - hatj + 2hatk) + t(hati + 2hatj +hatk)`.A. `5x + y + 3z = -4`B. `5x + y+ 3z =4`C. `5x -y - 3z = -4`D. `3x-y -z =2` |
| Answer» Correct Answer - D | |
| 40. |
The equation of plane containing the lines `barr=(2hatj-3hatk)+lamda(hati+2hatj+3hatk)` `barr=(2hati+6hatj+3hatk)+lamda(2hati+3hatj+4hatk)`A. `x-2y-z=0`B. `x-2y+z=0`C. `x+2y-z=0`D. `x+2y+z=0` |
| Answer» Correct Answer - B | |
| 41. |
The angle between the line `barr=(hati+2hatj-hatk)+lamda(hati-hatj+hatk)` and the plane `barr.(2hati-hatj+hatk)=5 isA. `"sin"^(-1)((4sqrt(2))/(3))`B. `"sin"^(-1)((2sqrt(2))/(3))`C. `"sin"^(-1)((2)/(3sqrt(2)))`D. `"sin"^(-1)((2sqrt(3))/(6))` |
| Answer» Correct Answer - B | |
| 42. |
The equation of plane passing through the intersection of the planes `barr.(hati+hatj+hatk)=2and barr.(2hati+3hatj+hatk)=4` and parallel to X - axis isA. `barr.(-hatj+hatk)=0`B. `barr.(hatj+hatk)=0`C. `barr.(-hatj+hatk)=4`D. `barr.(-hatj+hatk)=-2` |
| Answer» Correct Answer - A | |
| 43. |
The vector equation of the plane passing through the intersection of the planes `barr.(hati+hatj+hatk)=8 and barr. (2hati+3hatj+4hatk)=3` and the point (1 , 0 , 2 ) isA. `barr.(17hati+22hatj+27hatk)=71`B. `barr.(17hati+22hatj+27hatk)=41`C. `barr.(11hati+16hatj+21hatk)=71`D. `barr.(11hati+16hatj+21hatk)=41` |
| Answer» Correct Answer - A | |
| 44. |
The angle between the line `barr=(hati+hatj-hatk)+lamda(hati-hatj+hatk)` and the plane `barr.(hati-2hatj+3hatk)=5` isA. `"sin"^(-1)((6)/sqrt(7))`B. `"sin"^(-1)((6)/sqrt(21))`C. `"sin"^(-1)((6)/sqrt(7))`D. `"sin"^(-1)((7)/sqrt(6))` |
| Answer» Correct Answer - C | |
| 45. |
Let a plane passing through point `(-1 ,1 ,1)` is parallel to the vector `2hati+3hatj-7hatk` and the line `barr=(hati-2hatj-hatk)+lamda(3hati-8hatj+2hatk)` . The vector equation of plane isA. `barr.(2hati+hatj+hatk)=2`B. `barr.(2hati+hatj+hatk)=0`C. `barr.(2hati-hatj-hatk)=2`D. `barr.(2hati-hatj-hatk)=0` |
| Answer» Correct Answer - B | |
| 46. |
If the line `vecr=(hati-2hatj+3hatk)+lambda(2hati+hatj+2hatk)` is parallel to the plane `vecr(3hati-2hatj+mhatk)=10` then value of m isA. 2B. `-2`C. 4D. `-4` |
| Answer» Correct Answer - B | |
| 47. |
If the lines ` x = 1 + s, y = - 3 - lamda s , z = 1 + lamda s and x = ( t ) / ( s ) , y = 1 + t , z = 2 - t ` are coplanar, then ` lamda ` is equal toA. 2B. `-2`C. 0D. 1 |
| Answer» Correct Answer - B | |
| 48. |
The angle between two planes isA. the angles between the lines parallel to the planes from any point .B. the angle between the tangents to them from any pointC. the angle between the normals to them from any point.D. the angle between the lines perpendicular or parallel to the planes from any point. |
| Answer» Correct Answer - C | |
| 49. |
If the line `bar(r)=bar(a)+lamdabar(b)` is parallel to the plane `bar(r).bar(n)=p,` thenA. `bar(b).bar(n)=0`B. `bar(b).bar(n)=p`C. `bar(b)xxbar(n)=0`D. `bar(b)xxbar(n)=bar(a)` |
| Answer» Correct Answer - A | |
| 50. |
If the equation of two lines are given by `bar(r)=bar(a_(1))+lamdabar(b_(1))andbar(r)=bar(a_(2))+mubar(b_(2))` , where `lamda and mu` are parmater , then the angle `theta` between the lines isA. `"cos"theta=(bar(a_(1)).bar(b_(2)))/(|bar(a_(1))||bar(b_(2))|)`B. `"cos"theta=(bar(a_(2)).bar(b_(1)))/(|bar(a_(2))||bar(b_(1))|)`C. `"cos"theta=(bar(b_(1)).bar(b_(2)))/(|bar(b_(1))||bar(b_(2))|)`D. `"cos"theta=(bar(a_(1)).bar(a_(2)))/(|bar(a_(1))||bar(a_(2))|)` |
| Answer» Correct Answer - C | |