Question

The line $\frac{x - 2}{3} = \frac{y - 3}{4} = \frac{z - 4}{5}$ is parallel to the plane

• A. $2x + 3y + 4z = 29$
• B. $3x + 4y - 5z = 10$
• C. $3x + 4y + 5z = 38$
• D. $x + y + z = 0$

Answer 1

Answer: (B)

$3x + 4y - 5z = 10$

Answer 2

Conversely, From option (1) $\Rightarrow 3 \times 2 + 4 \times 3 + 5 \times 4 \neq 0$

From option (2) $\Rightarrow 3 \times 3 + 4 \times 4 - 5 \times 5 = 0$.