CBSE 2024 · Region 2 · Set 2 · Q27 · 3 marks
If vectors $\displaystyle \vec{\mathrm{a}}, \vec{\mathrm{b}}$ and $\displaystyle 2 \vec{\mathrm{a}}+3 \vec{\mathrm{b}}$ are unit vectors, then find the angle between $\displaystyle \overrightarrow{\mathrm{a}}$ and $\displaystyle \overrightarrow{\mathrm{b}}$.
Marking-scheme solution
$$\begin{aligned}
& |\vec{\mathrm{a}}|=|\vec{\mathrm{b}}|=|2 \vec{\mathrm{a}}+3 \vec{\mathrm{b}}|=1
& (2 \vec{\mathrm{a}}+3 \vec{\mathrm{b}})^{2}=|2 \vec{\mathrm{a}}+3 \vec{\mathrm{b}}|^{2}
\end{aligned}Hence, $\displaystyle \theta=\pi$
Vector AlgebraProduct of Two VectorsApplyshort_answermedium
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CBSE Class 12 Mathematics past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.