Question

The projection of the line $\frac{x+1}{-1}=\frac{y}{2}=\frac{z-1}{3}$ on the plane x – 2y + z = 6 is the line of intersection of this plane with the plane

• A. 2x + y + 2 = 0
• B. 3x + y – z = 2
• C. 2x – 3y + 8z = 3
• D. 2x - y + 2 = 0

Answer 1

The correct option is A 2x + y + 2 = 0

Equation of plane through (–1, 0, 1) is
a(x + 1) + b(y – 0) + c(z – 1) = 0 . . . .(i)
Which is parallel to given line and perpendicular to given plane

– a + 2b + 3c = 0 . . . .(ii)
and a – 2b + c = 0 . . . .(iii)
From Eqs. (ii) and (iii), c = 0, a = 2b
From Eqs. (i), 2b(x + 1) + by = 0
$\Rightarrow$ 2x + y + 2 = 0