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The position vectors of four points $P, Q, R, S$ are $2 \mathbf{a}+4 \mathbf{c}, \quad 5 \mathbf{a}+3 \sqrt{3} \mathbf{b}+4 \mathbf{c},-2 \sqrt{3} \mathbf{b}+\mathbf{c}$ and $2 \mathbf{a}+\mathbf{c}$ respectively, then
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Verified Answer
The correct answer is:
$\overrightarrow{P Q}$ is parallel to $\overrightarrow{R S}$
$\overrightarrow{P Q}=3 \mathbf{a}+3 \sqrt{3} \mathbf{b}$ and $\overrightarrow{R S}=2 \mathbf{a}+2 \sqrt{3} \mathbf{b}$
Hence $\overrightarrow{P Q }~||~ \overrightarrow{R S}$
Hence $\overrightarrow{P Q }~||~ \overrightarrow{R S}$
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