Question

The equation of the plane containing the line `(x + 1)/(-3) = (y - 3)/2 = (z + 2)/1` and the point (0, 7, –7), is ______.

Options

• x + y + z = 2

• x + y + z = 3

• x + y + z = 0

• None of these

Answer 1

The equation of the plane containing the line `(x + 1)/(-3) = (y - 3)/2 = (z + 2)/1` and the point (0, 7, –7), is x + y + z = 0.

Explanation:

Any plane containing `(x + 1)/(-3) = (y - 3)/2 = (z + 2)/1` is

a(x +  1) + b(y – 3) + c(z + 2) = 0  ...(i)

where – 3a + 2b + c = 0  ...(ii)

If the plane passes through (0, 7, –7).

∴ a + 4b – 5c = 0  ...(iii)

From Equation (ii) and (iii),

`a/(-10 - 4) = b/(1 - 15) = c/(-12 - 2)`

`\implies a/1 = b/1 = c/1`

Therefore, the plane (i) becomes

(x + 1) + (y – 3) + (z + 2) = 0

`\implies` x + y + z = 0