CBSE 2024 · Region 5 · Set 3 · Q30 · 3 marks
Find the projection of vector ( $\displaystyle \vec{\mathrm{b}}+\vec{\mathrm{c}}$ ) on vector $\displaystyle \vec{a}$, where $\displaystyle \vec{a}=2 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$, $\displaystyle \overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\displaystyle \overrightarrow{\mathrm{c}}=\hat{\mathrm{i}}+\hat{\mathrm{k}}$.
Marking-scheme solution
$$\vec{\mathrm{b}}+\vec{\mathrm{c}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}
Projection of $\displaystyle (\vec{\mathrm{b}}+\vec{\mathrm{c}})$ on $\displaystyle \vec{a}=\frac{(\vec{\mathrm{b}}+\vec{\mathrm{c}}) \cdot \vec{a}}{|\vec{a}|}=\frac{4+6+2}{\sqrt{4+4+1}}$
=4
$$
Vector AlgebraProduct of Two VectorsApplyshort_answereasy
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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.