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Vector equation of the plane passing through $a, b$ and parallel to the line $r = c + α d$ is

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$[r b - a d] = [a b c]$

$[r b - a d] = [a b d]$

$[r b - c a] = [a b d]$

$[r c - a b] = [a c d]$

answer is B.

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Detailed Solution

$\begin{array}{rcl} [r - a b - a d] & = & 0 \end{array}$

$\Rightarrow \begin{array}{rcl} [r b - a d] \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} [a b - a d] \end{array} \begin{array}{rcl} \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} [a b d] \end{array}$

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