NCERT Class 12-Mathematics: Chapter –11 Three Dimensional Geometry Part 9
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Question 18:
Find the length and the foot of perpendicular from the point to the plane .
Answer:
Equation of the given plane is …(i)
So, the equation of line through and parallel to is given by
If this point lies on the given plane, then
Question 19:
Find the equations of the line passing through the point and parallel to the planes and .
Answer:
Question 20:
Find the equation of the plane through the points and , and perpendicular to the plane .
Answer:
Question 21:
Find the shortest distance between the lines given by
Answer:
We have
Also,
Now, shortest distance between two lines is given by
Now,
And
Question 22:
Find the equation of the plane which is perpendicular to the plane and which contains the line of intersection of the planes and .
Answer:
Question 23:
The plane is rotated about its line of intersection with the plane through an angle . Prove that the equation of the plane in its new position is
Answer:
Equation of the plane is