Find the equation of a plane which passes through the point (3, 2, 0) and contains the line
Given that, a plane is passes through the point (3, 2, 0) so equation will be
a(x – 3) + b(y – 2) + c(z – 0) = 0
a(x – 3) + b(y – 2) + cz = 0 ……(1)
plane also contains the line
so it pass through the point (3, 2, 0)
a(3 – 3) + b(6 – 2) + c(4) = 0
4b + 4c = 0 …… (2)
Also plane will be parallel to,
a(1) + b(5) + c(4) = 0
a + 5b + 4c = 0 ……(3)
solving (2) and (3) by cross multiplication,
a = – k, b = k, c = – k
put a = – k, b = k, c = – k in equation (i) we get
(– k)(x – 3) + (k)(y – 2) + (– k)z = 0
– x + 3 + y – 2 – z = 0
x – y + z – 1 = 0