# MCQs for Mathematics Class 12 with Answers Chapter 11 Three Dimensional Geometry

Students of class 12 Mathematics should refer to MCQ Questions Class 12 Mathematics Three Dimensional Geometry with answers provided here which is an important chapter in Class 12 Mathematics NCERT textbook. These MCQ for Class 12 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 12 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 12 Mathematics examination

**Chapter 11 Three Dimensional Geometry MCQ with Answers Class 12 Mathematics**

MCQ Questions Class 12 Mathematics Three Dimensional Geometry provided below have been prepared by expert teachers of grade 12. These objective questions with solutions are expected to come in the upcoming Standard 12 examinations. Learn the below provided MCQ questions to get better marks in examinations.

**Question. The co-ordinates of the foot of the perpendicular drawn from the point (2, –3, 4) on the y-axis is**

(a) (2, 3, 4)

(b) (– 2, – 3, – 4)

(c) (0, –3, 0)

(d) (2, 0, 4)

## Answer

C

**Question. The coordinates of the foot of the perpendicular drawn form the origin to the plane****2x+3y+4z-12=0 is **

(a) (36/29, 24/29, 48/29)

(b) (24/29, 48/29, 36/29)

(c) (24/29, 36/29, 48/29)

(d) None of these

## Answer

C

**Question. The angle between a line whose direction ratios are in the ratio 2 : 2 : 1 and a line joining (3, 1, 4) to (7, 2, 12) is**

(a) cos^{-1}(2/3)

(b) cos^{-1}(2/3)

(c) tan ^{-1}(2/3 ) − 1

(d) None of these

## Answer

A

**Question. The equation of the plane through the intersection of the planes 3x -y +2z -4 = 0 and x + y + z -2 =0 and the point (2, 2, 1) is**

(a) 7x +5y +4z +8 =0

(b) 7x +5y +4z -8 =0

(c) 7x -5y +4z -8 =0

(d) None of these

## Answer

C

**Question. The equation of the plane that passes through the points (1,1,0) (1,2,1) and (-2,2-1 ) is**

(a) 2x +3y -3z = 5

(b) 2x +3y +3z =5

(c) 2x -3y +3z =5

(d) None of these

## Answer

A

**Question. The angle between the planes whose vector equation**

(a) cos^{−1}(15/√731)

(b) cos^{−1}(15/√7)

(c) π/4

(d) π/2

## Answer

A

**Question. Two planes 7x+ 5y +6z+30=0 and 3x-y-10z+4=0 are **

(a) non-parallel, perpendicular and have an angle π/2.

(b) parallel, non-perpendicular and have an angle 0.

(c) non-parallel, non-perpendicular and have an angle cos^{−1}(2/5

(d) non-parallel, non-perpendicular and have an angle cos^{−1}(1/5)

## Answer

C

**Question. The distance of the point (3, 2,1) − from the plane 2x-y+2z+3=0 s,**

(a) 3/13unit

(b) 13/3 units

(c) 3 units

(d) 2 units

## Answer

B

**Question. The equation of the plane through the line of intersection of the planes x +y +z = 1 and 2x +3y +4z =5 which is perpendicular to the plane x- y+ z =0 is,**

(a) -x +z +2 =0

(b) x -z +2 =0

(c) x -z -2 =0

(d) −x +z -2 =0

## Answer

B

**Question. The coordinates of the point where the line through (5,1,6) and (3,4,1) cross the YZ-plane, is **

(a) (0,-17/2,13/2)

(b) (0,17/2,-13/2)

(c) (0,5/2,7/2)

(d) (0,-5/2,7/2)

## Answer

B

**Question. If O be the origin and the coordinates of P be (1,2,–3), then the equation of the plane passing through P and perpendicular to OP is, **

(a) x+2y – 3z -14 = 0

(b) x-2y + 3z -14 = 0

(c) x+ 2y+ 3z -14= 0

(d) None of these

## Answer

A

**Question. Distance between the two planes 2x +3y + 4z=4 and 4x+ 6y +8z =12 is **

(a) 2 units

(b) 4 units

(c) 8 units

(d) 2/√29 units

## Answer

D

**Question. The equation of the plane which is perpendicular to the plane 5x+ 3y+6z+8=0 and which contains the line of intersection of the planes x+2y+3z-4=0 and 2x+y-z+5=0 **

(a) 23x+15y+50z+173=0

(b) 51x+15y+50z+173=0

(c) 51x+15y-50z+173=0

(d) None of the above

## Answer

C

**Question. **

## Answer

C

**Question. The planes 2x-y+ 4z = 5 and 5x-25y + 10z =6 are**

(a) perpendicular

(b) parallel

(c) intersect along Y-axis

(d) passes through (0, 0,5/4)

## Answer

C

**Question. The points (0,-1, -1), (-4,4,4), (4,5,1) and (3,9,4) are **

(a) collinear

(b) coplanar

(c) forming a square

(d) forming a triangle

## Answer

B

**Question. If (p _{1},q_{1},r_{1}) be the image of (p, q, r) in the plane ac+ by+ cz+d=0, then **

(a) p

_{1}-p/a = q

_{1}-q/b = r

_{1}-r/c

(b) a(p+p

_{1})+b (q+q

_{1})+ c(r+

_{1})+2d=0

(c) both (a) and (b)

(d) All of the above

## Answer

C

**Question. The cartesian equation of the plane perpendicular to the line x-1/2 = y-3/-/ = z-4/2 and passing through the origin is**

(a) 2x -y+ 2z −7 =0

(b) 2x +y+2z =0

(c) 2x-y+2z =0

(d) 2x-y-z =0

## Answer

C

**Question. If a plane meets the coordinate axes in A,B,C such that the centroid of the triangle is the point (1,r,r ^{2}), then equation of the plane is**

(a) x+ ry+ r

^{2}z = 3r

^{2}

(b) r

^{2}x ry+ z=3r

^{2}

(c) x+ ry+ r

^{2}z=3

(d) r

^{2}x ry+ z=3

## Answer

B

**Question. The equation of the right bisecting plane of the segment joining the points ( a, a ,a ) and (-a,-a,-a), a ≠ 0 is**

(a) x+ y+ z =a

(b) x+ y+ z=3a

(c) x+ y+ z =0

(d) x+ y+ z +a=0

## Answer

C

**Question. The reflection of the point (2,-1,3) in the plane 3x -2y-z=9 is**

(a) (26/7,15/7,17/7)

(b) (26/7, -15/7 , 17/7)

(c) 16/7,26/7,-17/7)

(d) (1/6, 2/3, 3/4)

## Answer

B

**Question. The equation of the plane through P( x _{1}, y_{1}, z_{1}) and perpendicular to OP, (O being the origin) is**

(a) xx

_{1}+ yy

_{1}+ zz

_{1}=x

_{1}+ y

_{1}

(b) xx

_{1}+ yy

_{1}+ zz

_{1}=y

_{1}+ z

_{1}

(c) xx

_{1}+ yy

_{1}+ zz

_{1}=x

^{2}

_{1}+ y

^{2}

_{1}+z

^{2}

_{1}

(d) xx

_{1}+ yy

_{1}= z+ z

_{1 }

## Answer

C

**Question. The shortest distance between the lines given by****r = (8 + 3λ) it – (9 + 16λ) jt + (10 + 7λ)kt and r = 15î + 29ĵ + 5k̂+ n(3î + 8ĵ – 5k̂) is**

(a) 7 units

(b) 2 units

(c) 14 units

(d) 3 units

## Answer

C

**Question. Distance of the point (a, b, c) from y-axis is**

(a) b

(b) b

(c) b + c

(d) a2 + c2

## Answer

D

**Question. The intercepts made by the plane 2x –3y + 5z + 4 = 0 on the coordinate axes are**

(a) – 2, 4/3 and -4/5

(b) – 2, –4/3 and 4/5

(c) 4/3 ,-4/3 and 7/3

(d) – 2, –4/3 and -4/5

## Answer

A

**Question. If the direction cosines of a line are k, k, k then**

(a) k > 0

(b) 0 < k < 1

(c) k = 1

(d) k = 1/√3or –1/√3

## Answer

D

**Question. The distance of the plane r .(2/7î +3/7ĵ -6/7k̂)= 1 from the origin is**

(a) 1

(b) 7

(c) 1/7

(d) none of these

## Answer

A

**Question. The area of the quadrilateral ABCD where A (0, 4, 1), B (2, 3, –1), C (4, 5, 0) and D (2, 6, 2) is equal to**

(a) 9 sq units

(b) 18 sq units

(c) 27 sq units

(d) 81 sq units

## Answer

A

**Question. The reflection of the point (α, β, γ) in the xy-plane is**

(a) (α, β, 0)

(b) (0, 0, c)

(c) (–α, –b, c)

(d) (α, b, –c)

## Answer

D

**Question. P is a point on the line segment joining the points (3, 2, –1) and (6, 2, –2). If x co-ordinate of P is 5, then its y co-ordinate is**

(a) 2

(b) 1

(c) –1

(d) –2

## Answer

A

**Question. The co-ordinates of the foot of perpendicular drawn from point A(1, 8, 4) to the line joining the points B(0, –1, 3) and C(2, –3, –1) are**

(a) (-7/3, 2/3, 11/3)

(b) (-5/3, 2/3, 19/3)

(c) (4/3, 2/3, 11/3)

(d) None of these

## Answer

B

**Question. If a, b, c are the angles that a line makes with the positive direction of x, y, z axis, respectively, then the direction cosines of the line are**

(a) sin α, sin β, sin γ

(b) cos α, cos β, cos γ

(c) tan α, tan β, tan γ

(d) cos2 α, cos2 β, cos2 γ

## Answer

B

**Question. The distance of a point P (a, b, c) from x-axis is**

(a) √(a2 + c2)

(b) √(a2 + b2)

(c) √(b2 + c2)

(d) √(b2 + c2)

## Answer

C

**Question. The equations of x-axis in space are**

(a) x = 0, y = 0

(b) x = 0, z = 0

(c) x = 0

(d) y = 0, z = 0

## Answer

D

**Question. A line makes equal angles with co-ordinate axis. Direction cosines of this line are**

(a) ± (1, 1, 1)

(b) ± (1/√3, 1/√3, 1/√3)

(c) ± (1/3, 1/3, 1/3)

(d) ± (1/√3,-1/√3,-1/√3)

## Answer

B

**Question. P is the point on the line segment joining the points (3, 2, –1) and (6, 2, –2). If x co-ordinate of P is 5, then its y co-ordinate is**

(a) 2

(b) 1

(c) –1

(d) –2

## Answer

A

**Question. The two planes x – 2y + 4z = 10 and 18x + 17y + kz = 50 are perpendicular, if k is equal to**

(a) –4

(b) 4

(c) 2

(d) – 2

## Answer

B

**Question. P is the point on the line segment joining the points (3, 2, –1) and (6, 2, –2). If x co-ordinate of P is 5, then its y co-ordinate is**

(a) 2

(b) 1

(c) –1

(d) –2

## Answer

A

**Question. The sine of the angle between the straight line x-2/3 = y-3/4 =z-4/5 and the plane 2x – 2y + z = 5 is**

(a) 10/√65

(b) 4/5√2

(c) 2√3/5

(d) √2/10

## Answer

D

**Question. The image of the point (1, 6, 3) in the line x/1 = y-1/2 = z-2/2 is**

(a) (2, 0, 5)

(b) (1, 3, 4)

(c) (1, 0, 7)

(d) (– 3, – 2, 0 )

## Answer

C

**Question. The coordinates of the point where the line through (3, – 4, – 5) and (2, –3, 1) crosses the plane passing through three points (2, 2, 1), (3, 0, 1) and (4, – 1, 0) are**

(a) (0, – 2, 7)

(b) (3, – 2, 5)

(c) (1, – 2, – 7)

(d) (1, – 2, 7)

## Answer

D

We hope the above multiple choice questions for Class 12 Mathematics for Chapter 11 Three Dimensional Geometry provided above with answers based on the latest syllabus and examination guidelines issued by CBSE, NCERT and KVS are really useful for you. Three Dimensional Geometry is an important chapter in Class 12 as it provides very strong understanding about this topic. Students should go through the answers provided for the MCQs after they have themselves solved the questions. All MCQs have been provided with four options for the students to solve. These questions are really useful for benefit of class 12 students. Please go through these and let us know if you have any feedback in the comments section.