# NCERT Class 12-Mathematics: Chapter –11 Three Dimensional Geometry Part 3

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**Question 7:**

Find the coordinates of the point where the line through and crosses the plane passing through three points and

**Answer:**

Equation of plane through three points and is

i.e.

Equation of line through and is

Any point on line is . This point lies on plane . Therefore, , i.e.,

Hence the required point is .

## Long Answer (L.A.)

**Question 8:**

Find the distance of the point from the point of intersection of the line and the plane.

**Answer:**

We have

Solving these two equations, we get which gives .

Therefore, the point of intersection of line and the plane is and the other given point is . Hence the distance between these two points is 13

**Question 9:**

A plane meets the co-ordinates axis in such that the centroid of the is the point . Show that the equation of the plane is

**Answer:**

Let the equation of the plane be

Then the co-ordinate of are and respectively. Centroid of the is

But co-ordinates of the centroid of the are (given).

Therefore,

Thus, the equation of plane is

**Question 10:**

Find the angle between the lines whose direction cosines are given by the equations: and .

**Answer:**

Eliminating *m* from the given two equations, we get

Now if *,* then

and if *,* then *.*

Thus the direction ratios of two lines are proportional to and ,

i.e. and .

So, vectors parallel to these lines are

, respectively.

If is the angle between the lines, then

Hence,