Question

The plane containing the point $(3, 2, 0)$ and the line $\frac{x - 3}{1} = \frac{y - 6}{5} = \frac{z - 4}{4}$ is

• A. $x - y + z = 1$
• B. $x + y + z = 5$
• C. $x + 2y - z = 1$
• D. $2x - y + z = 5$

Answer 1

The Correct Option is A

The direction ratios of the given line are $(1, 5, 4)$. The equation of the plane passing through the point $(3, 2, 0)$ with normal perpendicular to the direction ratios can be written as: \[ x - y + z = d. \] Substitute the point $(3, 2, 0)$: \[ 3 - 2 + 0 = d \implies d = 1. \] Thus, the equation is: \[ x - y + z = 1. \]