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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

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Detailed Solution

Vector $(3 \hat{i} - 2 \hat{j} + \hat{k}) \times (4 \hat{i} - 3 \hat{j} + 4 \hat{k})$ is perpendicular to $2 \hat{i} - \hat{j} + m \hat{k}$

$\Rightarrow |\begin{array}{l} 3 & - 2 & 1 \\ 4 & - 3 & 4 \\ 2 & - 1 & m \end{array}| = 0 \Rightarrow m = - 2$

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