NCERT Class 12-Mathematics: Chapter – 11 Three Dimensional Geometry Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

Doorsteptutor material for NCO is prepared by world's top subject experts: fully solved questions with step-by-step explanation- practice your way to success.

11.2 Solved Examples

Short Answer (S. A)

Question 1: If the direction ratios of a line are , find the direction cosines of the line.

Answer:

The direction cosines are given by

Here are respectively.

Therefore,

are D. C՚s of the line.

Question 2:

Find the direction cosines of the line passing through the points and .

Answer:

The direction cosines of a line passing through the points and are

Here

Hence D. C. ′ s are

Question 3: If a line makes an angle of with the positive direction of , respectively, then find its direction cosines.

Answer:

The direction cosines of a line which makes an angle of with the , are

Therefore, D. C. ′ s of the line are i.e.. ,

Question 4:

The coordinate of a point on the line joining the points and is . Find its coordinate.

Answer:

Let the point P divide in the ratio , then the co-ordinate of are

But coordinate of P is . Therefore,

Hence, the coordinate of is

Question 5: Find the distance of the point whose position vector is from the plane

Answer:

Here

So, the required distance is

Question 6:

Find the distance of the point from the line

Fig. 11.1-Find the Distance of the Point

Answer:

Here is the given point.

Any point on the line is given by ,

.

Since , we have

Thus

Hence .