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


Equation of plane through three points and is


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.


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


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).


Thus, the equation of plane is

Question 10:

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


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


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