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Mathematics · 2023 · 2 marks
CBSE 2023 · Region 3 · Set 1 · Q21
If r =3 i -2 j +6 k, find the value of ( r × j ) ·( r × k )-12.
If $\displaystyle \overrightarrow{\mathrm{r}}=3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+6 \hat{\mathrm{k}}$, find the value of $\displaystyle (\overrightarrow{\mathrm{r}} \times \hat{\mathrm{j}}) \cdot(\overrightarrow{\mathrm{r}} \times \hat{\mathrm{k}})-12$.
Marking-scheme solution
$$\begin{aligned}
& (\vec{\mathrm{r}} \times \hat{\mathrm{j}}) \cdot(\vec{\mathrm{r}} \times \hat{\mathrm{k}})-12=(3 \hat{\mathrm{k}}-6 \hat{\mathrm{i}}) \cdot(-3 \hat{\mathrm{j}}-2 \hat{\mathrm{i}})-12 \\
& =12-12=0
\end{aligned}
$$
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