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Three Dimensional Geometry Class 12 Multiple Choice Test

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Three Dimensional Geometry Class 12 (121101)


General Instruction:

1. There are 10 MCQ’s in the Test.

2. Passing %age is 50.

3. After time gets over, test will be submitted itself.

1 / 10

class 12 three dimensional geometry mcq

2 / 10

The shortest distance between two skew lines is given by:

a) The length of a perpendicular segment between the lines

b) The magnitude of the cross product of their direction vectors

c) The magnitude of the dot product of their direction vectors

d) The difference in their direction ratios

3 / 10

class 12 three dimensional geometry mcq

4 / 10

Which equation represents the vector equation of a line passing through points \( P(1,1,1) \) and \( Q(2,2,2) \)?

a) \( r = \langle 1,1,1 \rangle + \lambda \langle 1,1,1 \rangle \)

b) \( r = \langle 1,1,1 \rangle + \lambda \langle 2,2,2 \rangle \)

c) \( r = \langle 1,1,1 \rangle + \lambda \langle 1,2,1 \rangle \)

d) \( r = \langle 1,1,1 \rangle + \lambda \langle 1,1,2 \rangle \)

5 / 10

Which equation represents the Cartesian equation of a line passing through points \( P(1,2,3) \) and \( Q(4,5,6) \)?

a) \( \frac{x-1}{3} = \frac{y-2}{3} = \frac{z-3}{3} \)

b) \( \frac{x-1}{4} = \frac{y-2}{5} = \frac{z-3}{6} \)

c) \( \frac{x-1}{3} = \frac{y-2}{3} = \frac{z-3}{4} \)

d) \( \frac{x-1}{4} = \frac{y-2}{5} = \frac{z-3}{6} \)

6 / 10

How is the shortest distance between two skew lines typically determined?

a) Using vector addition.

b) Through scalar triple product.

c) Via vector cross product.

d) With vector dot product.

7 / 10

If the direction cosines of a line are \( \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \), what can be concluded about the line?

a) The line is parallel to the x-axis.

b) The line is parallel to the y-axis.

c) The line is parallel to the z-axis.

d) The line passes through the origin.

8 / 10

Skew lines are:

a) Parallel lines

b) Coplanar lines

c) Intersecting lines

d) Non-intersecting and non-parallel lines

9 / 10

The direction cosines of a line are given by:

a) Ratios of its coordinates

b) Components of its equation

c) Ratios of its coefficients

d) Components of its direction vector

10 / 10

The direction ratios of a line are determined by:

a) Ratios of its equation coefficients

b) Components of its direction vector

c) Ratios of its coordinates

d) Components of its equation

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