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If $A B C D$ is a parallelogram and the position vectors of $A, B, C$ are $\mathbf{i}+3 \mathbf{j}+5 \mathbf{k}, \mathbf{i}+\mathbf{j}+\mathbf{k}$ and $7 \mathbf{i}+7 \mathbf{j}+7 \mathbf{k}$, then the position vector of $D$ will be
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The correct answer is:
$7 \mathbf{i}+9 \mathbf{j}+11 \mathbf{k}$
Let position vector of $D$ is $x \mathbf{i}+y \mathbf{j}+\mathbf{z} \mathbf{k}$, then $\overrightarrow{A B}=\overrightarrow{D C} \Rightarrow-2 \mathbf{j}-4 \mathbf{k}=(7-x) \mathbf{i}+(7-y) \mathbf{j}+(7-z) \mathbf{k}$ $\Rightarrow x=7, y=9, z=11$.
Hence position vector of $D$ will be $7 \mathbf{i}+9 \mathbf{j}+11 \mathbf{k}$.
Hence position vector of $D$ will be $7 \mathbf{i}+9 \mathbf{j}+11 \mathbf{k}$.
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