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Mathematics · 2023 · 2 marks
CBSE 2023 · Region 4 · Set 2 · Q25
If a =4 i - j + k and b =2 i -2 j + k, then find a unit vector along the vector a × b.
If $\displaystyle \vec{\mathrm{a}}=4 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\displaystyle \vec{\mathrm{b}}=2 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$, then find a unit vector along the vector $\displaystyle \overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}$.
Marking-scheme solution
$\displaystyle \overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}=\left|\begin{array}{ccc} \hat{\boldsymbol{\imath}} & \hat{\boldsymbol{\jmath}} & \widehat{\boldsymbol{\mathrm{k}}} \\ \mathbf{4} & -\mathbf{1} & \mathbf{1} \\ \mathbf{2} & -\mathbf{2} & \mathbf{1} \end{array}\right|=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}$
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