If the vectors \overset{\rightarrow}{AB} = 3 \hat{i} + 4 \hat{k} \textrm{ }\textrm{ } and \textrm{ }\textrm{ } \overset{\rightarrow}{AC} = 5 \hat{i} - 2 \hat{j} + 4 \hat{k} are the sides of a triangle ABC, then the length of the median through A is :

Engineering

Mathematics

Vector Addition and Subtraction

Question

If the vectors $\vec{AB} = 3 \hat{i} + 4 \hat{k} and \vec{AC} = 5 \hat{i} - 2 \hat{j} + 4 \hat{k}$ are the sides of a triangle ABC, then the length of the median through A is :

$\sqrt{72}$

$\sqrt{33}$

$\sqrt{45}$

$\sqrt{18}$

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$| \vec{AD} | = | \frac{\vec{AB} + \vec{AC}}{2} |$

$= | \frac{8 \hat{i} - 2 \hat{j} + 8 \hat{k}}{2} |$

$= \sqrt{33}$