First slide

Algebra of vectors

Question

If 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 $∆$ ABC, then the length of the median through A is

Moderate

A

$\sqrt{14}$
B

$\sqrt{18}$
C

$\sqrt{29}$
D

5

Solution

$\begin{array}{l} \vec{AB} + \vec{AC} = 2 \vec{AD} \\ ∴ \vec{AD} = \frac{1}{2} {(- 3 \hat{i} + 4 \hat{k}) + (5 \hat{i} - 2 \hat{j} + 4 \hat{k})} \\ = \hat{i} - \hat{j} + 4 \hat{k} \end{array}$
$Length of A D = \sqrt{1 + 1 + 16} = \sqrt{18}$

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