# NCERT Class 12-Mathematics: Chapter –11 Three Dimensional Geometry Part 2

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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 .