CBSE 2026 · Region 4 · Set 1 · Q24 · 2 marks
If the position vectors of three points $\displaystyle \mathrm{A}, \mathrm{B}$ and C are $\displaystyle 3 \hat{\mathrm{i}}+\hat{\mathrm{j}}$, $\displaystyle 5 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}-3 \hat{k}$ and $\displaystyle 4 \hat{\mathrm{j}}$ respectively, then show that they form an isosceles triangle.
Marking-scheme solution
$\displaystyle \overrightarrow{AB}=2 \hat{i}+5 \hat{j}-3 \hat{k}, \overrightarrow{BC}=-5 \hat{i}-2 \hat{j}+3 \hat{k}, \overrightarrow{CA}=3 \hat{i}-3 \hat{j}$
Now, $\displaystyle |\overrightarrow{AB}|=|\overrightarrow{BC}|=\sqrt{38}$ units, $\displaystyle |\overrightarrow{CA}|=\sqrt{18}$ units
As, $\displaystyle |\overrightarrow{AB}|=|\overrightarrow{BC}|$ & sum of two sides is greater than the third
so, given points form an isosceles triangle.
Vector AlgebraProduct of Two 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.