# NCERT Class 12-Math's: Chapter –11 Three Dimensional Geometry Part 6

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Question 22:

If a line makes an angle of with each of and axis, then the angle which it makes with axis is _________

Let it makes angle with axis. Then which after simplification gives

## State Whether the Following Statements Are True or False in Examples 23 and 24

Question 23:

The points and are collinear.

Let A, B, C be the points , and , respectively. Then, the direction ratios of each of the lines AB and BC are proportional to . Therefore, the statement is true.

Question 24:

The vector equation of the line passing through the points and is

The position vector of the points and are , and therefore, the required equation of the line is given by

Hence, the statement is true.

## 11.3 EXERCISE

Question 1:

Find the position vector of a point A in space such that is inclined at to OX and at to OY and units.

Question 2:

Find the vector equation of the line which is parallel to the vector and which passes through the point

Question 3:

Show that the lines intersect. Also, find their point of intersection.

Question 4:

Find the angle between the lines

Question 5:

Prove that the line through and intersects the line through and .