Question

What will be the equation of plane passing through a point (1, 4, – 2) and parallel to the given plane – 2x + y – 3z = 9?

Options

• 2x – y + 3z + 8 = 0

• 2x = y + 3z + 8 = 0

• 2x – 2y + 2z + 10 = 0

• 2x + 2y – 3z + 8 = 0

Answer 1

2x – y + 3z + 8 = 0

Explanation:

`r . (2hati - 3hatj + 5hatk) + 2` = 0

Equation of plane parallel to the given plane is

–2x + y – 3z = λ  ...(i)

Since, plane (i) passes through the point (1, 4, –2).

Therefore this point satisfies the given plane.

Put x = 1, y – 4 and z = – 2 in equation (i)

–2(1) + 4 – 3(–2) = λ

–2 + 4 + 6 = λ

λ = 8

Put λ = 8 in equation (i), we get

–2x + y – 3z = 8

2x – y + 3z + 8 = 0