CBSE 2022 · Region 4 · Set 3 · Q8 · 3 marks
If $\displaystyle \overrightarrow{\mathrm{a}}=2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$ and $\displaystyle \overrightarrow{\mathrm{c}}=\hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}$ and the projection of vector $\displaystyle \vec{\mathrm{c}}+\lambda \vec{\mathrm{b}}$ on vector $\displaystyle \vec{\mathrm{a}}$ is $\displaystyle 2 \sqrt{6}$, then find the value of $\displaystyle \lambda$.
Marking-scheme solution
According to question
\[\begin{aligned}
& \frac{(\vec{c}+\lambda \vec{b}) \cdot \vec{a}}{|\vec{a}|}=2 \sqrt{6} \\
& \Rightarrow \frac{\vec{c} \cdot \vec{a}+\lambda \vec{b} \cdot \vec{a}}{\sqrt{6}}=2 \sqrt{6}
\end{aligned}
\]
\[\Rightarrow-2+\lambda(-1)=12
\]
\(\displaystyle \Rightarrow \lambda=-14\)
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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.