First slide

Planes in 3D

Question

$The value of m for which straight line 3 x - 2 y + z + 3 = 0 = 4 x - 3 y + 4 z + 1 is parallel to the plane$
$2 x - y + m z - 2 = 0 is$

Moderate

A

-2
B

8
C

-18
D

11

Solution

$Vector ((3 \hat{i} - 2 \hat{j} + \hat{k}) \times (4 \hat{i} - 3 \hat{j} + 4 \hat{k})) is perpendicular to$
$\begin{array}{l} 2 \hat{i} - \hat{j} + m \hat{k} . Thus, \\ |\begin{array}{lll} 3 & - 2 & 1 \\ 4 & - 3 & 4 \\ 2 & - 1 & m \end{array}| = 0 or m = - 2 \end{array}$

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