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Mathematics · 2026 · 2 marks
CBSE 2026 · Region 4 · Set 2 · Q24
If ( 2 i +3 j + k ) and ( 2 i + j - k ) represent the sides A B and A C respectively of Δ ABC, find the vector representing the median through A.
If ( $\displaystyle 2 \hat{i}+3 \hat{j}+\hat{k}$ ) and ( $\displaystyle 2 \hat{i}+\hat{j}-\hat{k}$ ) represent the sides $\displaystyle \overrightarrow{A B}$ and $\displaystyle \overrightarrow{A C}$ respectively of $\displaystyle \Delta \mathrm{ABC}$, find the vector representing the median through A.
Marking-scheme solution
$\displaystyle \overrightarrow{AB}+\overrightarrow{AC}=4 \hat{i}+4 \hat{j}+0 \hat{k}$
Now, $\displaystyle \overrightarrow{AD}=\dfrac{\overrightarrow{AB}+\overrightarrow{AC}}{2}=2 \hat{i}+2 \hat{j}+0 \hat{k}$
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