The value of p such that the vectors $i + 3 j - 2 k, 2 i - j + 4 k$ and $3 i + 2 j + p k$ are coplanar is

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Solution

The correct option is B 2
$i + 3 j - 2 k, 2 i - j + 4 k$ and $3 i + 2 j + p k$ are coplanar
$\Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} 1 & 3 & - 2 2 & - 1 & 4 3 & 2 & p \end{matrix} ∣ ∣ ∣ ∣ = 0$
$\Rightarrow (- p - 8) - 3 (2 p - 12) - 14 = - 7 p + 14 = 0$
$∴ p = 2$
Hence, option B.

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