Find the equation of family of planes through the line of intersection of the planes 3x – y + 2z = 4 and x + y + z = 2 which is passing through (2, 2, 1)?

Question

Find the equation of family of planes through the line of intersection of the planes 3x – y + 2z = 4 and x + y + z = 2 which is passing through (2, 2, 1) ?

Philoid · Accepted Answer

The equation of the family of planes through the line of intersection of planes

3x – y + 2z = 4 and x + y + z = 2 is,

(3x – y + 2z – 4) + k(x + y + z – 2) = 0 ……(1)

If it passes through (2, 2, 1) then,

(6 – 2 + 2 – 4) + k(2 + 2 + 1 – 2) = 0

k = –

Substituting k = – in eq.(1) We get,

7x – 5y + 4z = 0 as the equation of the required plane.