Class 12 Mathematics - Chapter 11: Three Dimensional Geometry MCQ Questions

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Your Class 12 Mathematics Study Path

Question 1

2x – y + z + 3 = 0 is the line:

A (frac { x+3 }{3}) = (frac { y-5 }{1}) = (frac { z-2 }{-5})

B (frac { x-3 }{-3}) = (frac { y+5 }{-1}) = (frac { z-2 }{5})

C (frac { x-3 }{3}) = (frac { y+5 }{1}) = (frac { z-2 }{-5})

D (frac { x+3 }{-3}) = (frac { y-5 }{-1}) = (frac { z+2 }{5})

Question 2

The planes 2x – y + 4z = 3 and 5x – 2.5y +10 z = 6 are

A passes through (0, 0, (frac { 5 }{4}))

B intersect along y-axis

C parallel

D perpendicular

Question 3

If the angle between the line x = (frac { y-1 }{2}) = (frac { z-3 }{Î»}) and the plane x + 2y + 3z = 4is cos^-1 ((sqrt{frac { 5}{14}})) then Î», equals:

A (frac { 5 }{3})

B (frac { 2 }{5})

C (frac { 3 }{2})

D (frac { 2 }{3})

Question 4

The equation of the plane containing the line: 2x – 5y + z = 3; x + y + 4z = 5 and parallel to the plane: x + 3y + 6z = 1 is:

A 2x + 6y – 12z = -13.

B x + 3y + 6z = 7

C x + 3y + 6z = – 7

D 2x + 6y+ 12z = 13

Question 5

An equation of a plane parallel to the plane x – 2y + 2z – 5 = 0 and at a unit distance from the origin is:

A x – 2y + 2z + 5 = 0.

B x – 2y + 2z – 1 = 0

C x – 2y + 2z + 1 = 0

D x – 2y + 2z – 3 = 0

Question 6

The length of the perpendicular drawn from the point (3, -1, 11) to the line (frac { x }{2}) = (frac { y-2 }{3}) = (frac { z-3 }{4}) is

A (sqrt { 65})

B (sqrt { 53})

C (sqrt { 33})

D (sqrt { 29})

Question 7

(frac { x-2 }{3}) = (frac { y+1 }{4}) = (frac { z-2 }{12}) and flie plane x – y + z = 16 is

A 13.

B 3(sqrt { 21 })

C 8

D 2(sqrt { 14 })

Question 8

A line AB in three-dimensional space makes angles 45Â° and 120Â° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle Î¸ with the positive z-axis, then Î¸ equals:

A 15Â°.

B 60Â°

C 45Â°

D 30Â°

Question 9

2x + 3y + 4z = 5 and 4x + 6y + 8z = 12 is

A (frac { 1 }{sqrt{29}}) units.

B 8 units

C 4 units

D 2 units

Question 10

If the lines: (frac { x-2 }{1}) = (frac { y-3 }{1}) = (frac { z-4 }{-k}) and (frac { x-1 }{k}) = (frac { y-4 }{2}) = (frac { z-5 }{1}) are coplanar, then k can have:

A any value.

B exactly three values

C exactly two values

D exactly one value

Question 11

2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

A (frac { 3 }{2})

B (frac { 9 }{2})

C (frac { 7 }{2})

D (frac { 5 }{2})

Question 12

The projections of a vector on the three co-ordinate axes are 6, -3, 2 respectively. The direction-cosines of the vector are:

A 6, -3, 2.

B (frac { -6 }{7}), (frac { -3 }{7}), (frac { 1 }{7})

C (frac { 6 }{7}), –(frac { 3}{7}), (frac { 2 }{7})

D (frac { 6 }{5}), –(frac { 3 }{5}), (frac { 2 }{5})

Question 13

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

A bÂ² + cÂ².

B (sqrt { b^2+c^2})

C (sqrt { a^2+b^2})

D (sqrt { a^2+c^2})

Question 14

The reflection of the point (Î±, ÃŸ, Î³) in the xy-plane is:

A (Î±, ÃŸ, -Î³).

B (-Î±, -ÃŸ, Î³)

C (0, 0, Î³)

D (Î±, ÃŸ, 0)

Question 15

3x + 5y + 7z = 3 and 9x + 15y + 21z = 9?

A 6.

B (frac { 6 }{sqrt{83}})

C 3

Question 16

If Î±, ÃŸ, Î³ 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 < cosÂ² Î±, cosÂ² ÃŸ, cosÂ² Î³ >.

B < tan Î±, tan ÃŸ, tan Î³ >

C < cos Î±, cos ÃŸ, cos Î³ >

D < sin Î±, sin ÃŸ, sin Î³ >

Question 17

The co-ordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are given by:

A (0, 5, 7).

B (0, 0, 7)

C (0, 5, 0)

D (2, 0, 0)

Question 18

The equation of the line in vector form passing through the point (-1, 3, 5) and parallel to line (frac { x-3 }{2}) = (frac { y-4 }{3}), z = 2 is

A (vec r) = (2(hat i) + 3(hat j)]) + Î»(-(hat i) + 3(hat j) + 5(hat k)).

B (vec r) = (2(hat i)+ 3(hat j) – 2(hat k)) + Î»(-(hat i) + 3(hat j) + 5(hat k))

C (vec r) = (-(hat i)+ 3(hat j) + 5(hat k)) + Î»(2(hat i) + 3(hat j))

D (vec r) = (-(hat i) + 3(hat j) + 5(hat k)) + Î»(2(hat i) +3(hat j) + (hat k))

Question 19

Let the line (frac { x-2 }{3}) = (frac { y-1 }{-5}) = (frac { z-2 }{2}) lie in the plane x + 3y – Î±z + ÃŸ = 0. Then (Î±, ÃŸ) equals:

A (6, -17).

B (-5, 5)

C (5, -15)

D (-6, -17)

Question 20

If the direction-cosines of a line are < k, k, k >, then

A k = (frac { 1 }{âˆš3}) or –(frac { 1 }{âˆš3})

B k = 1

C 0 < k < 1

D k > 0

Question 21

The distance of the point (1, -5, 9) from the plane x – y + z = 5, measured along a straight line x = y = z is:

A 3âˆš5

B 3(sqrt {10})

C 5âˆš3

D 10âˆš3

Question 22

If the line (frac { x-3 }{2}) = (frac { y+2 }{-1}) = (frac { z+4 }{3}) lies in the plane lx + my – z = 9,then lÂ² + mÂ² is equal to

A 26.

B 2

C 5

D 18

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Class 12 Mathematics - Chapter 11: Three Dimensional Geometry MCQ Questions

Your Class 12 Mathematics Study Path

2x – y + z + 3 = 0 is the line:

The planes 2x – y + 4z = 3 and 5x – 2.5y +10 z = 6 are

If the angle between the line x = (frac { y-1 }{2}) = (frac { z-3 }{Î»}) and the plane x + 2y + 3z = 4is cos^-1 ((sqrt{frac { 5}{14}})) then Î», equals:

The equation of the plane containing the line: 2x – 5y + z = 3; x + y + 4z = 5 and parallel to the plane: x + 3y + 6z = 1 is:

An equation of a plane parallel to the plane x – 2y + 2z – 5 = 0 and at a unit distance from the origin is:

The length of the perpendicular drawn from the point (3, -1, 11) to the line (frac { x }{2}) = (frac { y-2 }{3}) = (frac { z-3 }{4}) is

(frac { x-2 }{3}) = (frac { y+1 }{4}) = (frac { z-2 }{12}) and flie plane x – y + z = 16 is

A line AB in three-dimensional space makes angles 45Â° and 120Â° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle Î¸ with the positive z-axis, then Î¸ equals:

2x + 3y + 4z = 5 and 4x + 6y + 8z = 12 is

If the lines: (frac { x-2 }{1}) = (frac { y-3 }{1}) = (frac { z-4 }{-k}) and (frac { x-1 }{k}) = (frac { y-4 }{2}) = (frac { z-5 }{1}) are coplanar, then k can have:

2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

The projections of a vector on the three co-ordinate axes are 6, -3, 2 respectively. The direction-cosines of the vector are:

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

The reflection of the point (Î±, ÃŸ, Î³) in the xy-plane is:

3x + 5y + 7z = 3 and 9x + 15y + 21z = 9?

If Î±, ÃŸ, Î³ 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:

The co-ordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are given by:

The equation of the line in vector form passing through the point (-1, 3, 5) and parallel to line (frac { x-3 }{2}) = (frac { y-4 }{3}), z = 2 is

Let the line (frac { x-2 }{3}) = (frac { y-1 }{-5}) = (frac { z-2 }{2}) lie in the plane x + 3y – Î±z + ÃŸ = 0. Then (Î±, ÃŸ) equals:

If the direction-cosines of a line are < k, k, k >, then

The distance of the point (1, -5, 9) from the plane x – y + z = 5, measured along a straight line x = y = z is:

If the line (frac { x-3 }{2}) = (frac { y+2 }{-1}) = (frac { z+4 }{3}) lies in the plane lx + my – z = 9,then lÂ² + mÂ² is equal to

Practice Complete!

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Class 12 Mathematics - Chapter 11: Three Dimensional Geometry MCQ Questions

Your Class 12 Mathematics Study Path

2x – y + z + 3 = 0 is the line:

The planes 2x – y + 4z = 3 and 5x – 2.5y +10 z = 6 are

If the angle between the line x = (frac { y-1 }{2}) = (frac { z-3 }{Î»}) and the plane x + 2y + 3z = 4is cos-1 ((sqrt{frac { 5}{14}})) then Î», equals:

The equation of the plane containing the line: 2x – 5y + z = 3; x + y + 4z = 5 and parallel to the plane: x + 3y + 6z = 1 is:

An equation of a plane parallel to the plane x – 2y + 2z – 5 = 0 and at a unit distance from the origin is:

The length of the perpendicular drawn from the point (3, -1, 11) to the line (frac { x }{2}) = (frac { y-2 }{3}) = (frac { z-3 }{4}) is

(frac { x-2 }{3}) = (frac { y+1 }{4}) = (frac { z-2 }{12}) and flie plane x – y + z = 16 is

A line AB in three-dimensional space makes angles 45Â° and 120Â° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle Î¸ with the positive z-axis, then Î¸ equals:

2x + 3y + 4z = 5 and 4x + 6y + 8z = 12 is

If the lines: (frac { x-2 }{1}) = (frac { y-3 }{1}) = (frac { z-4 }{-k}) and (frac { x-1 }{k}) = (frac { y-4 }{2}) = (frac { z-5 }{1}) are coplanar, then k can have:

2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

The projections of a vector on the three co-ordinate axes are 6, -3, 2 respectively. The direction-cosines of the vector are:

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

The reflection of the point (Î±, ÃŸ, Î³) in the xy-plane is:

3x + 5y + 7z = 3 and 9x + 15y + 21z = 9?

If Î±, ÃŸ, Î³ 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:

The co-ordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are given by:

The equation of the line in vector form passing through the point (-1, 3, 5) and parallel to line (frac { x-3 }{2}) = (frac { y-4 }{3}), z = 2 is

Let the line (frac { x-2 }{3}) = (frac { y-1 }{-5}) = (frac { z-2 }{2}) lie in the plane x + 3y – Î±z + ÃŸ = 0. Then (Î±, ÃŸ) equals:

If the direction-cosines of a line are < k, k, k >, then

The distance of the point (1, -5, 9) from the plane x – y + z = 5, measured along a straight line x = y = z is:

If the line (frac { x-3 }{2}) = (frac { y+2 }{-1}) = (frac { z+4 }{3}) lies in the plane lx + my – z = 9,then lÂ² + mÂ² is equal to

Practice Complete!

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If the angle between the line x = (frac { y-1 }{2}) = (frac { z-3 }{Î»}) and the plane x + 2y + 3z = 4is cos^-1 ((sqrt{frac { 5}{14}})) then Î», equals: