Find the equation of the plane through the point and passing through the line of intersection of the planes and

Question

Find the equation of the plane through the point  and passing through the line of intersection of the planes  and

Philoid · Accepted Answer

we know that, the equation of a plane passing through the line of intersection of two planes

and

is given by

So the equation of the plane passing through the line of intersection of given two planes

and is given by

…… (1)

As given that, plane (1) is passing through the point 2 so

(2)(1) + (1)(3) + ( – 1)( – 1) + k[(2)(0) + (1)(1) + ( – 1)(2)] = 0

(2 + 3 + 1) + k(1 – 2) = 0

6 – k = 0

k = 6

put the value of k in equation (1)

So, the equation of the required plane is