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

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## 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

**Answer**:

Here is the given point.

Any point on the line is given by ,

.

Since , we have

Thus

Hence .