CBSE 2026 · Region 2 · Set 1 · Q24 · 2 marks
If $\displaystyle \overrightarrow{\mathrm{AB}}=\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\displaystyle \overrightarrow{\mathrm{AC}}=3 \hat{\mathrm{i}}-\hat{\mathrm{j}}+4 \hat{\mathrm{k}}$ represent the two vectors along the sides AB and AC of $\displaystyle \triangle \mathrm{ABC}$, prove that the median $\displaystyle \overrightarrow{\mathrm{AD}}=\frac{\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{AC}}}{2}$, where D is midpoint of BC. Hence, find the length of median AD.
Marking-scheme solution
Considering $\displaystyle A$ as the origin, $\displaystyle \overrightarrow{AB}$ and $\displaystyle \overrightarrow{AC}$ are p.v. of $\displaystyle B$ and $\displaystyle C$ respectively.
Hence p.v. of the mid point $\displaystyle D$ is $\displaystyle \dfrac{\overrightarrow{AB}+\overrightarrow{AC}}{2}$
So, $\displaystyle \overrightarrow{AD}=\dfrac{(\hat{\jmath}+\hat{k})+(3\hat{\imath}-\hat{\jmath}+4\hat{k})}{2}$
$\displaystyle \overrightarrow{AD}=\dfrac{3\hat{\imath}+5\hat{k}}{2}$
$\displaystyle \left|\overrightarrow{AD}\right|=\dfrac{1}{2}\sqrt{3^{2}+5^{2}}=\dfrac{\sqrt{34}}{2}$
Vector AlgebraAddition of VectorsApplyvery_short_answermedium
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CBSE Class 12 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.