Question

Consider a plane x + y - z = 1 and the point A(1, 2, -3). A line L has the equation x = 1 + 3r, y = 2 – r, z = 3 + 4r.
Equation of the plane containing the line L and the point A has the equation

• A. x - 3y + 5 = 0
• B. x + 3y - 7 = 0
• C. 3x - y - 1 = 0
• D. 3x + y - 5 = 0

Answer 1

The correct option is B

x + 3y - 7 = 0

Equation of plane containing the line L is
A(x - 1) + B(y - 2) + C (z - 3) = 0
Where 3A - B + 4C = 0 ..... (1)
$\therefore$ (1) also contain the point A(1, 2, -3)
Hence C = 0; 3A = B
Equation of plane = x - 1 + 3(y - z) = 0
x + 3y - 7 = 0