Question

Let the line `(x - 2)/3 = (y - 1)/(-5) = (z + 2)/2` lie in the plane x + 3y - αz + β = 0. Then, (α, β) equals ______ 

Options

• (6, -17)

• (-6, 7)

• (5, -15)

• (-5, 5)

Answer 1

Let the line `(x - 2)/3 = (y - 1)/(-5) = (z + 2)/2` lie in the plane x + 3y - αz + β = 0. Then, (α, β) equals (-6, 7).

Explanation:

Point (2, 1, -2) lies in the plane

 x + 3y - αz + β = 0

∴ 2 + 3(1) - α(-2) + β = 0

⇒ 2α + β = -5 ....................(i)

Also, the d.r.s of the normal is perpendicular to the given plane. 

∴ 3(1) + (-5)(3) + (2)(-α) = 0

⇒ 3 - 15 - 2α = 0

⇒ α = -6

Substituting the value of α in equation (i), we get β = 7