First slide

Planes in 3D

Question

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

Easy

A

$2 x + y - 2 z = 0$
B

$3 x + 4 y + 5 z = 7$
C

$x + y + z = 2$
D

$2 x + 3 y + 4 z = 0$

Solution

The condition that the line $\frac{x - x_{1}}{l} = \frac{y - y_{1}}{m} = \frac{z - z_{1}}{n}$ is parallel to the plane $a x + b y + c z + d = 0$ is $a l + b m + c n = 0$
Here $l = 3, m = 4, n = 5$ and verify each option for which $a l + b m + c n = 0$
This is matching with the option (1) $(\sin c e 3 (2) + 4 (1) + 5 (- 2) = 0)$

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