The two vectors j + k and 3 i - j + 4 k represent the two sides A… - Vidyadip

Question

The two vectors $\hat{\text{j}} + \hat{\text{k}}$ and $3\hat{\text{i}} - \hat{\text{j}} + 4\hat{\text{k}}$ represent the two sides AB and AC, respectively of a $\triangle \text{ABC},$ Find the length of the median through A.

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Answer

$\overrightarrow{\text{AD}} = \overrightarrow{\text{AB}} + \frac{1}{2}[\overrightarrow{\text{AC}} - \overrightarrow{\text{AB}}] = \frac{1}{2} (\overrightarrow{\text{AC}} + \overrightarrow{\text{AB}})$
$|\overrightarrow{\text{AD}}| =\frac{1}{2} |3\hat{\text{i}} + 5\hat{\text{k}}| = \frac{1}{2}\sqrt{34}$

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