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Mathematics · 2023 · 2 marks
CBSE 2023 · Region 1 · Set 1 · Q22
Find all the vectors of magnitude 3 √ 3 which are collinear to vector i + j + k.
Find all the vectors of magnitude $\displaystyle 3 \sqrt{3}$ which are collinear to vector $\displaystyle \hat{i}+\hat{j}+\hat{k}$.
Marking-scheme solution
$$\text { Unit vector along } \hat{i}+\hat{j}+\hat{k} \text { is } \frac{\hat{i}}{\sqrt{3}}+\frac{\hat{j}}{\sqrt{3}}+\frac{\hat{k}}{\sqrt{3}}
$$
Required vectors are $\displaystyle 3 \hat{i}+3 \hat{j}+3 \hat{k}$ and $\displaystyle -3 \hat{i}-3 \hat{j}-3 \hat{k}$
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