If \( \vec{a}, \vec{b}, \vec{c} \& \vec{d} \) are the pvs of the points \( \mathrm{A}, \mathrm{B...

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If \( \vec{a}, \vec{b}, \vec{c} \& \vec{d} \) are the pvs of the points \( \mathrm{A}, \mathrm{B}, \mathrm{C} \& \mathrm{D} \) respectively in three dimensional space \& satisfy the relation \( 3 \vec{a}-2 \vec{b}+\vec{c}-2 \vec{d}=0 \), then :
\( \mathrm{P} \)
(A) A, B, C \& D are coplanar
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(B) the line joining the points \( \mathrm{B} \& \mathrm{D} \) divides the line joining the point \( \mathrm{A} \& \mathrm{C} \) in the ratio \( 2: 1 \).
(C) the line joining the points A \& C divides the line joining the points B \& D in the ratio \( 1: 1 \)
(D) the four vectors \( \vec{a}, \vec{b}, \vec{c} \& \vec{d} \) are linearly dependent.
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