Question

Suppose the line `(x - 2)/α = ("y" - 2)/(-5) = ("z" + 2)/2` lies on the plane x + 3y – 2z + β = 0. Then (α + β) is equal to ______.

Options

• 6

• 7

• 8

• 9

Answer 1

Suppose the line `(x - 2)/α = ("y" - 2)/(-5) = ("z" + 2)/2` lies on the plane x + 3y – 2z + β = 0. Then (α + β) is equal to 7.

Explanation:

Since, given line lies in the plane

So, point (2, 2, –2) also lies on given plane

So, 2 + 3 × 2 –2 (–2) + β = 0

`\implies` 2 + 6 + 4 + β = 0

`\implies` β = –12

∵ Normal of plane perpendicular to the given line.

Also α × 1 – 5 × 3 + 2 × –2 = 0

`\implies` α – 15 – 4 = 0

`\implies` α = 19

∴ α + β = 19 – 12 = 7