CBSE 2022 · Region 3 · Set 2 · Q1 · 2 marks
Write the projection of the vector $\displaystyle (\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}})$ on the vector $\displaystyle \overrightarrow{\mathrm{a}}$, where $\displaystyle \overrightarrow{\mathrm{a}}=$ $\displaystyle 2 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}$ and $\displaystyle \overrightarrow{\mathrm{c}}=2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+4 \hat{\mathrm{k}}$.
Marking-scheme solution
\[\begin{aligned}
& \vec{b}+\vec{c}=3 \hat{\imath}+\hat{\jmath}+2 \hat{k} \\
& \text { Projection of } \vec{b}+\vec{c} \text { on } \vec{a}=\frac{(\vec{b}+\vec{c}) \cdot \vec{a}}{|\vec{a}|} \\
& \qquad=\frac{(3 \hat{i}+\hat{j}+2 \hat{k}) \cdot(2 \hat{i}-2 \hat{j}+\hat{k})}{\sqrt{9}} \\
& =\frac{6-2+2}{3}=\frac{6}{3}=2
\end{aligned}
\]
Vector AlgebraProduct of Two VectorsApplyvery_short_answereasy
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CBSE Class 12 Mathematics past-paper question from the 2022board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.