Please refer to the MCQ Questions for Class 12 Mathematics Chapter 11 Three Dimensional Geometry with Answers. The following Three Dimensional Geometry Class 12 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 12. Our experts have designed MCQ Questions for Class 12 Mathematics with Answers for all chapters in your NCERT Class 12 Mathematics book.

## Three Dimensional Geometry Class 12 MCQ Questions with Answers

See below Three Dimensional Geometry Class 12 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

**Question.** If the plane 2x – 3y + 6z – 11 = 0 makes an angle sin^{-1} a with X-axis, then the value of a is

(a) √3/2

(b) √2/3

(c) 2/7

(d) 3/7

**Answer**

C

**Question. A and B are two given points. Let C divides AB internally and D divides AB externally in the same ratio. Then, AC, AB and AD are in**

(a) AP

(b) GP

(c) HP

(d) None of these

**Answer**

C

**Question. The area of the triangle whose vertices are (1,0,1), (2,-1,3) and (-1,2,-1), is**

(a) 1

(b) 2

(c) 2

(d) None of these

**Answer**

C

**Question.2. A plane is such that the foot of perpendicular drawn from the origin to it is (2,-1,1). The distance of ( 1,2,3) from the plane is**

(a) √3/2

(b) 3 2/

(c) 2

(d) None of these

## Answer

B

**Question .The equation of the plane through (3,1,-3) and (1,2,2) and parallel to the line with DR’s1 ,1 ,-2 is**

(a) x- y+ z+1= 0

(b) x+ y- z + 1= 0

(c) x- y- z −1=0

(d) x +y+ z -1=0

**Answer**

D

**Question. A line makes an angle θ both with x and y-axes. A possible value of θ is i**

**Answer**

C

**Question. A plane passes through the point ( 1,-2,3) and is parallel to the plane 2x-2y+z=0. The distance of the point (-1,2,0) from the plane is **

(a) 2

(b) 3

(c) 4

(d) 5

**Answer**

D

**Question. The angle between a diagonal of a cube and an edge of the cube intersecting the diagonal is**

(a) cos−1 1/3

(b) cos−1 √2/3

(c) tan−1√2

(d) None of these

**Answer**

C

**Question. The image of the point A (1,0,0) in the line x-1/2 = y+1/-3 = z+10/8 is**

(a) (5,- 8,-4)

(b) (3,- 4, 2)

(c) (5,- 4,- 8)

(d) (3, 4 -2)

**Answer**

A

**Question. The d.r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle π/4 with plane x + y = 3 are**

(a) 1, √2 ,1

(b) 1, 1, √2

(c) 1, 1, 2

(d) √2 , 1, 1

**Answer**

B

**Question. Let L be the line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2z = 2. If L makes an angle α with the positive x-axis, then cos α equals**

(a) 1

(b) 1/2

(c) 1/3

(d) 1/2

**Answer**

C

**Question. The radius of the circle in which the sphere x ^{2} + y^{2} + z^{2} + 2x – 2y – 4z – 19 = 0 is cut by the plane x + 2y + 2z + 7 = 0 is**

(a) 4

(b) 1

(c) 2

(d) 3

**Answer**

D

**Question. The distance between the line r̅ = 2î – 2ĵ + 3k̂ + λ(î – ĵ + 4k̂) and the plane r̅ .(î + 5ĵ + k̂) = 5 îs**

(a) 10/9

(b) 10/3√3

(c) 3/10

(d) 10/3

**Answer**

B

**Question. If the plane 2ax – 3ay + 4a + 6 = 0 passes through the midpoint of the line oining the centres of the spheres x ^{2} + y^{2} + z^{2} + 6x – 8y – 2z = 13 and x^{2} + y^{2} + z^{2} – 10x + 4y – 2z = 8 then a equals**

(a) – 1

(b) 1

(c) – 2

(d) 2

**Answer**

C

**Question. Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is**

(a) 9/2

(b) 5/2

(c) 7/2

(d) 3/2

**Answer**

C

**Question. The line passing through the points (5, 1, a) and (3, b, 1) crosses the y -plane at the point (0, 17/2, -13/2). Then**

(a) a = 2, b = 8

(b) a = 4, b = 6

(c) a = 6, b = 4

(d) a = 8, b = 2

**Answer**

C

**Question. Two system of rectangular axes have the same origin. If a plane cuts them at distances a,b,c and a’,b’,c’ from the origin then**

(a) 1/a^{2} + 1/b^{2} + 1/c^{2} − 1/a’^{2} − 1/b’^{2} − 1/c’^{2} = 0

(b) 1/a^{2} + 1/b^{2} + 1/c^{2} + 1/a’^{2} + 1/b’^{2} + 1/c’^{2} = 0

(c) 1/a^{2} + 1/b^{2} − 1/c^{2} + 1/a’^{2} + 1/b’^{2} − 1/c’^{2} = 0

(d) 1/a^{2} − 1/b^{2} − 1/c^{2} + 1/a’^{2} − 1/b’^{2} − 1/c’^{2} = 0

**Answer**

A

**Question. The plane x + 2y – z = 4 cuts the sphere x ^{2} + y^{2} + z^{2} – x + z – 2 = 0 in a circle of radius**

(a) 3

(b) 1

(c) 2

(d) √2

**Answer**

B

**Question. The angle between a diagonal of a cube and an edge of the cube intersecting the diagonal is**

(a) cos−1 1/3

(b) cos−1 √2/3

(c) tan−1√2

(d) None of these

**Answer**

C

**Question. The projection of the line segment joining (2, 5, 6) and (3, 2, 7) on the line with direction ratios 2, 1,- 2 is**

(a) 1/2

(b) 1/3

(c) 2

(d) 1

**Answer**

D

**Question. The plane passing through the point (-2,-2,2) containing the line joining the points (1,-1,2)) and ( 1,1,1) makes intercepts on the coordinate axes and the sum of whose length is**

(a) 3

(b) 6

(c) 12

(d) 20

**Answer**

C

**Question. If the points ( 1,2,3) and (2,1,0 ) lie on the opposite sides of the plane 2x+3y-2z=k, then**

(a) k < 1

(b) k > 2

(c) k < 1or k > 2

(d) 1 2 < < k

**Answer**

D

**Question. OABC is a tetrahedron such that OA= OB= OC k and each of the edges OA, OB , and OC is inclined at an angle θ with the other two the range of θ is**

**Answer**

D

**Question. A variable plane at a distance of 1 unit from the origin coordinate axes at A, B and C. If the centroid D (x,y,z) of ∆ABC satisfies the relation 1/x ^{2}+ 1/y^{2} + 1/z^{2}= k, then k is equal to**

(a) 3

(b) 1

(c) 1/3

(d) 9

**Answer**

D

**Question. OABC is regular tetrahedron of unit edge. Its volume is**

(a) 1/√3

(b) 1/√6

(c) 1/3√2

(d) 1/6√2

**Answer**

D

**Question. Find the planes bisecting the acute angle between the planes x-y+2z+1=0 and 2x+y+z+2=0**

(a) x+ z -1=0

(b) x+ z +1=0

(c) x- z − 1=0

(d) None of these

**Answer**

B

**Question. If the orthocentre and centroid of a triangle are (-3,5,1) and (3,3,-1) respectively, then its circumcentre is**

(a) (6, 2, 2)

(b) (1, 2, 0)

(c) (6, 2, 2)

(d)(6, 2, 2)

**Answer**

A

**Question. Find the distance of the plane x+ 2y- z = 2 from the point (2,-1,3)) as measured in the direction with DR’s ( 2,2,1).**

(a) 2

(b) −3

(c) −2

(d) 3

**Answer**

D

**Question. Let L be the line of intersection of the planes 2x+3y +z=1 and x+ 3y+2z = 2. If L makes an angleα with the positive x-axis, thencos α is equal to**

(a) 1/2

(b) 1

(c) 1/√2

(d) 1/√3

**Answer**

D

**Question. If α, β, γ and δ are the angles between a straight line with the diagonals of a cube, then sin ^{2}α+ sin^{2}β+ sin^{2} γ+sin^{2} δ is equal to**

(a) 5/3

(b) 8/3

(c) 7/4

(d) None of these

**Answer**

A

**Question. The direction cosines to two lines at right angles are (1,2,3) and −(-2,1/2,1/3) ,then the direction cosine perpendicular to both the given lines are**

**Answer**

A

**Question. A equation of the plane passing through the points (3, 2, –1), (3, 4, 2) and (7, 0, 6) is 5x + 3y -2z= λ, where λ is**

(a) 23

(b) 21

(c) 19

(d) 27

**Answer**

A

**Question. A variable plane which remains at a constant distance pfrom the origin cuts the coordinate axes in A, B, C . The locus of the centroid of the tetrahedron OABC is y ^{2} z^{2} +z^{2} x^{2}+ x^{2} y^{2}=kx^{2}y^{2}z^{2}, where k is equal to**

(a) 9p

^{2}

(b) 9/p

^{2}

(c) 7/p

^{2}

(d) 16/αβϒ

**Answer**

D

**Question. The point on the line x-2/1 = y+3/-2 = z+5/-2 at a distance of 6 from the point (2, –3, –5) is**

(a) (3, –5, –3)

(b) (4, –7, –9)

(c) (0, 2, –1)

(d) (–3, 5, 3)

**Answer**

B

**Question. The distance of the point A(-2,3,1) ) from the line PQ through P(-3,5,2) which make equal angles with the axes is**

(a) 2/√3

(b) √14/3

(c) 16/√3

(d) 5/√3

**Answer**

B

**Question. The line joining the points (1, 1, 2) and (3, –2, 1) meets the plane 3x +2y+ z=6 the point**

(a) (1, 1, 2)

(b) (3, –2, 1)

(c) (2, –3, 1)

(d) ( 3, 2, 1)

**Answer**

B

**Question. The plane passing through the point (5, 1, 2) perpendicular to the line 2(x-2) = y- 4= z-5 will meet the line in the point**

(a) (1, 2, 3)

(b) (2, 3, 1)

(c) (1, 3, 2)

(d) (3, 2, 1)

**Answer**

A

**Question.**

**Answer**

C

**Question. A variable plane is at a constant distance p from the origin and meets the axes in A,B and C. Through A,B and C planes are drawn parallel to the coordinate planes, then the locus of their point of intersection is**

**Answer**

A

**Question. P, Q, R, and s are four coplanar points on the sides AB BC ,CD, and DA of a skew quadrilateral. The product AP/PB⋅ /BQ/QC⋅CR/RD⋅DS/SA is equal to**

(a) –2

(b) –1

(c) 2

(d) 1

**Answer**

D

**Question. The straight lines whose direction cosines l, m and n are given by the equations al +bm+ cn= 0,ul ^{2}+vm^{2}+ wn^{2} =0 are perpendicular or parallel according as**

**Answer**

C

**Question. If a variable line in two adjacent positions had direction cosines l, m and n and direction cosines for 2nd position.//30 then the small angle so between two positions is given by**

**Answer**

A

**Question. The angles between the four diagonals of a rectangular parallelopiped whose edges are a, b and c are**

**Answer**

B

**Question. The four planes my +nz= 0,nz+ lx =0, lx+ my+= 0and lx +my+ nz= p form a tetrahedron whose volume is**

(a) 3p^{3}/21mnm

(b) 2p^{3}/31mn

(c) 2p^{2}/31mn

(d) 3p^{2}/21mn

**Answer**

B

**Question. A triangle, the lengths of whose sides are a b, and c is placed so that the middle points of the sides are on the axes, then the equation to the plane is**

**Answer**

D

**Question. The direction cosines l, m, n of two lines which are connected by the relations l- 5m+3n=0 and 7l ^{2} + 5m^{2}-3n^{2}=0 are**

**Answer**

C

**Question. ABC is any triangle and O is any point in the plane of the triangle. AO, BO, CO meet the sides BC, CA, AB in D, E, F respectively, then OD/AD+OE/BE+OF/CF is equal to**

(a) 0

(b) −1

(c) 1

(d) 2

**Answer**

C

**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.**

(a) 1

(b) 7

(c) 1/7

(d) None of these

**Answer**

A

**Question. A plane which passes through the point (3, 2, 0) and the line (x – 4)/1 = (y – 7)/5 = (z – 4)/4 is**

(a) x – y + z =1

(b) x + y + z = 5

(c) x + 2y – z = 1

(d) 2x – y + z = 5

**Answer**

A

**Question. The shortest distance from the plane 12x + 4y +3z = 327 to the sphere x ^{2} + y^{2} + z^{2} + 4x – 2y – 6z = 155 is**

(a) 39

(b) 26

(c) 11(4/13)

(d) 13

**Answer**

D

**Question. If (2, 3, 5) is one end of a diameter of the sphere x ^{2} + y^{2} + z^{2} – 6x – 12y – 2z + 20 = 0, then the cooordinates of the other end of the diameter are**

(a) (4, 3, 5)

(b) (4, 3, – 3)

(c) (4, 9, – 3)

(d) (4, –3, 3)

**Answer**

C

**Question. If the angle θ between the line (x+1)/1 = (y – 1)/2 = (z – 2)/2 and the plane 2x – y + √λ z + 4 = 0 is such that sin θ = 1/3 then the value of λ is**

(a) 5/3

(b) -3/5

(c) 3/4

(d) -4/3

**Answer**

A

**Question. The intersection of the spheres x ^{2} + y^{2} + z^{2} + 7x – 2y – z = 13 and x^{2} + y^{2} + z^{2} – 3x + 3y + 4z = 8 is the same as the intersection of one of the sphere and the plane**

(a) 2x – y – z = 1

(b) x – 2y – z = 1

(c) x – y – 2z = 1

(d) x – y – z = 1

**Answer**

A

**Question. The image of the point (–1, 3, 4) in the plane x – 2y = 0 is**

(a) (– 17/3, – 19/3, 4)

(b) (15,11, 4)

(c) (– 17/3, – 19/3, 1)

(d) None of these

**Answer**

D

**Question.** The sine of the angle between the straight line

**and the plane 2x – 2y + z = 5 is**

**Answer**

D

**Question.** Distance of the point (α, β, γ) from Y-axis is

**Answer**

D

** Question. The reflection of the point (α, β, γ) in the XY -plane is**(a) (α, β, 0) (b)

(0, 0, γ)

(c) (-α, – β, – γ)

(d) (α, β, – γ)

**Answer**

D

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

**Answer**

D

** Question. The locus represented by xy + yz = 0 is**(a) a pair of perpendicular lines

(b) a pair of parallel lines

(c) a pair of parallel planes

(d) a pair of perpendicular planes

**Answer**

D

**True/False**

**Question.** The unit vector normal to the plane x + 2y + 3z – 6 = 0 is

**Answer**

True

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

**Answer**

True

**Question.**

**Answer**

False

**Question.** The equation of a line, which is parallel to 2î, + ĵ, + 3k̂ and which passes through the point (5, -2, 4) is

**Answer**

False

**Question.** If the foot of perpendicular drawn from the origin to a plane is (5, – 3, – 2), then the equation of plane is *r̅* (5î, – 3ĵ – 2k̂ ) = 38.

**Answer**

True

**Question.**

**Answer**

False

**Question.** The vector equation of the line

**Answer**

True

**Question.**

**Answer**

False