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

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11.2 Solved Examples

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 .