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If the vectors $\mathrm{AB}=-3 \mathbf{i}+4 \mathbf{k}$ and $\mathrm{AC}=5 \mathbf{i}-2 \mathbf{j}+4 \mathbf{k}$ are the sides of a $\triangle A B C$, then the length of the median through $A$ is
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The correct answer is:
$\sqrt{18}$
$\therefore$ Position vector of $\mathrm{AD}$
$\begin{aligned} & =\frac{1(-3 \mathbf{i}+4 \mathbf{k})+1(5 \mathbf{i}-2 \mathbf{j}+4 \mathbf{k})}{1+1} \\ & =\mathbf{i}-\mathbf{j}+4 \mathbf{k} \\ & \therefore|\mathrm{AD}|=\sqrt{1+1+16}=\sqrt{18}\end{aligned}$
$\begin{aligned} & =\frac{1(-3 \mathbf{i}+4 \mathbf{k})+1(5 \mathbf{i}-2 \mathbf{j}+4 \mathbf{k})}{1+1} \\ & =\mathbf{i}-\mathbf{j}+4 \mathbf{k} \\ & \therefore|\mathrm{AD}|=\sqrt{1+1+16}=\sqrt{18}\end{aligned}$
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