# NCERT Class 12-Mathematics: Chapter –11 Three Dimensional Geometry Part 4

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Question 11:

Find the co-ordinates of the foot of perpendicular drawn from the point to the line joining the points and .

Let L be the foot of perpendicular drawn from the points to the line passing through B and C as shown in the Fig. 11.2. The equation of line BC by using formula , the equation of the line BC is

Comparing both sides, we get

Thus, the co-ordinate of L are ,

so that the direction ratios of the line AL are , i.e.

Since AL is perpendicular to BC, we have,

The required point is obtained by substituting the value of , in , which is

Question 12:

Find the image of the point in the line

Let be the given point and let L be the foot of perpendicular from P to the given line.

The coordinates of a general point on the given line are

If the coordinates of L are , then the direction ratios of PL are .

But the direction ratios of given line which is perpendicular to PL are . Therefore, , which gives . Hence coordinates of L are .

Let be the image of in the given line. Then L is the mid-point of PQ. Therefore,

Hence, the image of in the given line is .

Question 13:

Find the image of the point having position vector in the plane

Let the given point be P and Q be the image of P in the plane as shown in the Fig. 11.4.