CBSE 2023 · Region 2 · Set 3 · Q21 · 2 marks
If points $\displaystyle \mathrm{A}, \mathrm{B}$ and C have position vectors $\displaystyle 2 \hat{\mathrm{i}}, \hat{\mathrm{j}}$ and $\displaystyle 2 \hat{\mathrm{k}}$ respectively, then show that $\displaystyle \triangle \mathrm{ABC}$ is an isosceles triangle.
Marking-scheme solution
$$\begin{aligned}
& \overrightarrow{\mathbf{B A}}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}} ; \overrightarrow{\mathbf{B C}}=2 \hat{\mathbf{k}}-\hat{\mathbf{j}} \\
& |\overrightarrow{\mathbf{B A}}|=|\overrightarrow{\mathbf{B C}}|=\sqrt{5} \Rightarrow \Delta \mathbf{A B C} \text { is an isosceles triangle }
\end{aligned}
$$
Vector AlgebraProduct of Two VectorsApplyvery_short_answereasy
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CBSE Class 12 Mathematics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.