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

Doorsteptutor material for IMO Class-11 is prepared by world's top subject experts: fully solved questions with step-by-step explanation- practice your way to success.

Download PDF of This Page (Size: 138K)

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,

Developed by: