Check the below NCERT MCQ Questions for Class 12 Maths Chapter 11 Three Dimensional Geometry with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Three Dimensional Geometry Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

## Three Dimensional Geometry Class 12 MCQs Questions with Answers

Question 1.

The direction cosines of the y-axis are

(a) (6, 0, 0)

(b) (1, 0, 0)

(c) (0, 1, 0)

(d) (0, 0, 1)

## Answer

Answer: (c) (0, 1, 0)

Question 2.

The direction ratios of the line joining the points (x, y, z) and (x_{2}, y_{2}, z_{1}) are

(a) x_{1} + x_{2}, y_{1} + y_{2}, z_{1} + z_{2}

(b) \(\sqrt{(x_1 – x_2)^2 + (y_1 – y_2)^2 + (z_1 + z_2)^2}\)

(c) \(\frac{x_1+x_2}{2}\), \(\frac{y_1+y_2}{2}\), \(\frac{z_1+z_2}{2}\)

(d) x_{2} – x_{1}, y_{2} – y_{1}, z_{2} – z_{1}

## Answer

Answer: (d) x_{2} – x_{1}, y_{2} – y_{1}, z_{2} – z_{1}

Question 3.

The coordinates of the midpoints of the line segment joining the points (2, 3, 4) and (8, -3, 8) are

(a) (10, 0, 12)

(b) (5, 6, 0)

(c) (6, 5, 0)

(d) (5, 0, 6)

## Answer

Answer: (d) (5, 0, 6)

Question 4.

If the planes a_{1}x + b, y + c, z + d_{1} = 0 and a_{2}x + b, y + c_{2}z + d_{2} = 0 are perpendicular to each other then

(a) \(\frac{a_1}{a_2}\) = \(\frac{b_1}{b_2}\) = \(\frac{c_1}{c_2}\)

(b) \(\frac{a_1}{a_2}\) + \(\frac{b_1}{b_2}\), \(\frac{c_1}{c_2}\)

(c) a_{1}a_{2} + b_{1}b_{2} + c_{1}c_{2} = 0

(d) a\(_{1}^{2}\)a\(_{2}^{2}\) + b\(_{1}^{2}\)b\(_{2}^{2}\) + c\(_{1}^{2}\)c\(_{2}^{2}\) = 0

## Answer

Answer: (c) a_{1}a_{2} + b_{1}b_{2} + c_{1}c_{2} = 0

Question 5.

The distance of the plane 2x – 3y + 6z + 7 = 0 from the point (2, -3, -1) is

(a) 4

(b) 3

(c) 2

(d) \(\frac{1}{5}\)

## Answer

Answer: (c) 2

Question 6.

The direction cosines of the normal to the plane 2x – 3y – 6z – 3 = 0 are

(a) \(\frac{2}{7}\), \(\frac{-3}{7}\), \(\frac{-6}{7}\)

(b) \(\frac{2}{7}\), \(\frac{3}{7}\), \(\frac{6}{7}\)

(c) \(\frac{-2}{7}\), \(\frac{-3}{7}\), \(\frac{-6}{7}\)

(d) None of these

## Answer

Answer: (a) \(\frac{2}{7}\), \(\frac{-3}{7}\), \(\frac{-6}{7}\)

Question 7.

If 2x + 5y – 6z + 3 = 0 be the equation of the plane, then the equation of any plane parallel to the given plane is

(a) 3x + 5y – 6z + 3 = 0

(b) 2x – 5y – 6z + 3 = 0

(c) 2x + 5y – 6z + k = 0

(d) None of these

## Answer

Answer: (c) 2x + 5y – 6z + k = 0

Question 8.

(2, – 3, – 1) 2x – 3y + 6z + 7 = 0

(a) 4

(b) 3

(c) 2

(d) \(\frac{1}{5}\)

## Answer

Answer: (c) 2

Question 9.

The length of the ⊥^{er} from the point (0, – 1, 3) to the plane 2x + y – 2z + 1 = 0 is

(a) 0

(b) 2√3

(c) \(\frac{2}{3}\)

(d) 2

## Answer

Answer: (d) 2

Question 10.

The shortest distance between the lines \(\vec{r}\) = \(\vec{a}\) + k\(\vec{b}\) and r = \(\vec{a}\) + l\(\vec{c}\) is (\(\vec{b}\) and \(\vec{c}\) are non-collinear)

(a) 0

(b) |\(\vec{b}\).\(\vec{c}\)|

(c) \(\frac{|\vec{b}×\vec{c}|}{|\vec {a}|}\)

(d) \(\frac{|\vec{b}.\vec{c}|}{|\vec {a}|}\)

## Answer

Answer: (a) 0

Question 11.

The equation xy = 0 in three dimensional space is represented by

(a) a plane

(b) two plane are right angles

(c) a pair of parallel planes

(d) a pair of st. line

## Answer

Answer: (b) two plane are right angles

Question 12.

The direction cosines of any normal to the xy plane are

(a) 1, 0 ,0

(b) 0, 1, 0

(c) 1, 1, 0

(d) 1, 1, 0

## Answer

Answer: (d) 1, 1, 0

Question 13.

How many lines through the origin in make equal angles with the coordinate axis?

(a) 1

(b) 4

(c) 8

(d) 2

## Answer

Answer: (c) 8

Question 14.

The direction cosines of the line joining (1, -1, 1) and (-1, 1, 1) are

(a) 2, -2, 0

(b) 1, -1, 0

(c) \(\frac{1}{√2}\), – \(\frac{1}{√2}\)

(d) None of these

## Answer

Answer: (c) \(\frac{1}{√2}\), – \(\frac{1}{√2}\)

Question 15.

The equation x² – x – 2 = 0 in three dimensional space is represented by

(a) A pair of parallel planes

(b) A pair of straight lines

(c) A pair of perpendicular plane

(d) None of these

## Answer

Answer: (a) A pair of parallel planes

Question 16.

The distance of the point (-3, 4, 5) from the origin

(a) 50

(b) 5√2

(c) 6

(d) None of these

## Answer

Answer: (b) 5√2

Question 17.

If a line makes angles Q_{1}, Q_{21} and Q_{3} respectively with the coordinate axis then the value of cos² Q_{1} + cos² Q_{2} + cos² Q_{3}

(a) 2

(b) 1

(c) 4

(d) \(\frac{3}{2}\)

## Answer

Answer: (b) 1

Question 18.

The direction ratios of a line are 1,3,5 then its direction cosines are

(a) \(\frac{1}{\sqrt{35}}\), \(\frac{3}{\sqrt{35}}\), \(\frac{5}{\sqrt{35}}\)

(b) \(\frac{1}{9}\), \(\frac{1}{3}\), \(\frac{5}{9}\)

(c) \(\frac{5}{\sqrt{35}}\), \(\frac{3}{\sqrt{35}}\), \(\frac{1}{\sqrt{35}}\)

(d) None of these

## Answer

Answer: (a) \(\frac{1}{\sqrt{35}}\), \(\frac{3}{\sqrt{35}}\), \(\frac{5}{\sqrt{35}}\)

Question 19.

The direction ratios of the normal to the plane 7x + 4y – 2z + 5 = 0 are

(a) 7, 4,-2

(b)7, 4, 5

(c) 7, 4, 2

(d) 4, -2, 5

## Answer

Answer: (a) 7, 4,-2

Question 20.

The direction ratios of the line of intersection of the planes 3x + 2y – z = 5 and x – y + 2z = 3 are

(a) 3, 2, -1

(b) -3, 7, 5

(c) 1, -1, 2

(d) – 11, 4, -5

## Answer

Answer: (b) -3, 7, 5

Question 21.

The lines of intersection of the planes \(\vec{r}\)(3\(\hat{i}\) – \(\hat{j}\) + \(\hat{k}\)) = 1 and \(\vec{r}\)(\(\hat{i}\) +4\(\hat{j}\) – 2\(\hat{k}\)) = 2 is parallel to the vector

(a) 2\(\hat{i}\) + 7\(\hat{j}\) + 13\(\hat{k}\)

(b) -2\(\hat{i}\) + 7\(\hat{j}\) + 13\(\hat{k}\)

(c) 2\(\hat{i}\) – 7\(\hat{j}\) + 13\(\hat{i}\)

(b) -2\(\hat{i}\) – 7\(\hat{j}\) – 13\(\hat{k}\)

## Answer

Answer: (b) -2\(\hat{i}\) + 7\(\hat{j}\) + 13\(\hat{k}\)

Question 22.

The equation of the plane through the origin and parallel to the plane 3x – 4y + 5z + 6 = 0

(a) 3x – 4y – 5z – 6 = 0

(b) 3x – 4y + 5z + 6 = 0

(c) 3x – 4y + 5z = 0

(d) 3x + 4y – 5z + 6 = 0

## Answer

Answer: (c) 3x – 4y + 5z = 0

Question 23.

The locus of xy + yz = 0 is

(a) A pair of st. lines

(b) A pair of parallel lines

(c) A pair of parallel planes

(d) A pair of perpendicular planes

## Answer

Answer: (d) A pair of perpendicular planes

Question 24.

The plane x + y = 0

(a) is parallel to z-axis

(b) is perpendicular to z-axis

(c) passes through z-axis

(d) None of these

## Answer

Answer: (c) passes through z-axis

Question 25.

If α, β, γ are the angle which a half ray makes with the positive directions of the axis then sin²α + sin²β + sin²γ =

(a) 1

(b) 2

(c) 0

(d) -1

## Answer

Answer: (b) 2

Question 26.

If a line makes angles α, β, γ with the axis then cos 2α + cos 2β + cos 2γ =

(a) -2

(b) -1

(c) 1

(d) 2

## Answer

Answer: (b) -1

Question 27.

The line x = 1, y = 2 is

(a) parallel to x-axis

(b) parallel to y-axis

(c) parallel to z-axis

(d) None of these

## Answer

Answer: (c) parallel to z-axis

Question 28.

The points A (1, 1, 0), B(0, 1, 1), C(1, 0, 1) and D(\(\frac{2}{3}\), \(\frac{2}{3}\), \(\frac{2}{3}\))

(a) Coplanar

(b) Non-coplanar

(c) Vertices of a parallelogram

(d) None of these

## Answer

Answer: (a) Coplanar

Question 29.

The angle between the planes 2x – y + z = 6 and x + y + 2z = 7 is

(a) \(\frac{π}{4}\)

(b) \(\frac{π}{6}\)

(c) \(\frac{π}{3}\)

(d) \(\frac{π}{2}\)

## Answer

Answer: (c) \(\frac{π}{3}\)

Question 30.

The distance of the points (2, 1, -1) from the plane x- 2y + 4z – 9 is

(a) \(\frac{\sqrt{31}}{21}\)

(b) \(\frac{13}{21}\)

(c) \(\frac{13}{\sqrt{21}}\)

(d) \(\sqrt{\frac{π}{2}}\)

## Answer

Answer: (c) \(\frac{13}{\sqrt{21}}\)

Question 31.

The planes \(\vec{r}\)(2\(\hat{i}\) + 3\(\hat{j}\) – 6\(\hat{k}\)) = 7 and

\(\vec{r}\)(\(\frac{-2}{7}\)\(\vec{i}\) – \(\frac{3}{j}\)\(\vec{j}\) + \(\frac{6}{7}\)\(\vec{k}\)) = 0 are

(a) parallel

(b) at right angles

(c) equidistant front origin

(d) None of these

## Answer

Answer: (a) parallel

Question 32.

The equation of the plane through point (1, 2, -3) which is parallel to the plane 3x- 5y + 2z = 11 is given by

(a) 3x – 5y + 2z – 13 = 0

(b) 5x – 3y + 2z + 13 = 0

(c) 3x – 2y + 5z + 13 = 0

(d) 3x – 5y + 2z + 13 = 0

## Answer

Answer: (d) 3x – 5y + 2z + 13 = 0

Question 33.

Distance of the point (a, β, γ) from y-axis is

(a) β

(b) |β|

(c) |β + γ|

(d) \(\sqrt{α^2+γ^2}\)

## Answer

Answer: (d) \(\sqrt{α^2+γ^2}\)

Question 34.

If the directions cosines of a line are A, k, k, then

(a) k > 0

(b) 0 < k < 1

(c) k = 1

(d) k = \(\frac{1}{√3}\) or –\(\frac{1}{√3}\)

## Answer

Answer: (d) k = \(\frac{1}{√3}\) or –\(\frac{1}{√3}\)

Question 35.

The distance of the plane \(\vec{r}\)(\(\frac{-2}{7}\)\(\hat{i}\) – \(\frac{3}{7}\)\(\hat{j}\) + \(\frac{6}{7}\)\(\hat{k}\)) = 0 from the orgin is

(a) 1

(b) 7

(c) \(\frac{1}{7}\)

(d) None of these

## Answer

Answer: (a) 1

Question 36.

The sine of the angle between the straight line \(\frac{x-2}{3}\) = \(\frac{y-3}{4}\) = \(\frac{z-4}{5}\) and the plane 2x – 2y + z = 5 is

(a) \(\frac{10}{6√5}\)

(b) \(\frac{4}{5√2}\)

(c) \(\frac{2√3}{5}\)

(d) \(\sqrt{\frac{√2}{10}}\)

## Answer

Answer: (c) \(\frac{2√3}{5}\)

Question 37.

The reflection of the point (a, β, γ) in the xy-plane is

(a) (α, β, 0)

(b) (0, 0, γ)

(c) (- α, – β, γ)

(d) (α, β, γ)

## Answer

Answer: (d) (α, β, γ)

Question 38.

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

Answer: (a) 9 sq. units

Question 39.

The plane 2x – 3y + 6z – 11 = 0 makes an angle sin^{-1} (α) with .e-axis. The value of a is equal to

(a) \(\frac{√3}{2}\)

(b) \(\frac{√2}{3}\)

(c) \(\frac{2}{7}\)

(d) \(\frac{3}{7}\)

## Answer

Answer: (c) \(\frac{2}{7}\)

Question 40.

The cosines of the angle between any two diagonals of a cube is

(a) \(\frac{1}{3}\)

(b) \(\frac{1}{2}\)

(c) \(\frac{2}{3}\)

(d) \(\frac{1}{√3}\)

## Answer

Answer: (a) \(\frac{1}{3}\)

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