# NCERT Class 12-Mathematics: Chapter –11 Three Dimensional Geometry Part 5

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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

.