NCERT Class 12-Mathematics: Chapter – 11 Three Dimensional Geometry Part 5 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Objective Type Questions

Choose the Correct Answer from the Given Four Options in Each of the Examples 14 to 19

Question 14:

The coordinates of the foot of the perpendicular drawn from the point on the axis are given by

(A)

(B)

(C)

(D)

Answer:

(A) is the correct answer.

Question 15:

P is a point on the line segment joining the points and . If co-ordinate of P is 5, then its y co-ordinate is

(A)

(B)

(C)

(D)

Answer:

(A) is the correct answer.

Let P divides the line segment in the ratio of coordinate of the point P may be expressed as giving so that

Question 16:

If are the angles that a line makes with the positive direction of axis, respectively, then the direction cosines of the line are.

(A)

(B)

(C)

(D)

Answer:

(B) is the correct answer.

Question 17:

The distance of a point from axis is

(A)

(B)

(C)

(D)

Answer:

(C) Is the correct answer. The required distance is the distance of from , which is .

Question 18:

The equations of axis in space are

(A)

(B)

(C)

(D)

Answer:

(D) Is the correct answer.

On axis the co-ordinate and co-ordinates are zero.

Question 19:

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

(A)

(B)

(C)

(D)

Answer:

(B) is the correct answer. Let the line makes angle α with each of the axis. Then, its direction cosines are .

Since . Therefore,

Fill in the Blanks in Each of the Examples from 20 to 22

Question 20:

If a line makes angles with axis, respectively, then its direction cosines are ________

Answer:

The direction cosines are

Question 21:

If a line makes angles with the positive directions of the coordinate axes, then the value of is ________

Answer:

Note that

.