NCERT Class 12-Mathematics: Chapter – 11 Three Dimensional Geometry Part 9 (For CBSE, ICSE, IAS, NET, NRA 2023)

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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