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

- 2

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8

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Solution

The correct option is B $- 2$
Normal of the straight line $3 x - 2 y + z + 3 = 0 = 4 x - 3 y + 4 z + 1$ is given by,
$(3^i - 2^j +^k) \times (4^i - 3^j + 4^k) = - 5^i - 8^j -^k$
Since, the straight line is parallel to plane $2 x - y + m z - 2 = 0$
Therefore, $(- 5^i - 8^j -^k) . (2^i -^j + m^k) = 0$

Since, dot product of the normal with the parallel line would be $0$ .
$\Rightarrow - 10 + 8 - m = 0$

$\Rightarrow m = - 2$
Ans: A

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