JEE MAIN - Mathematics (2023 - 30th January Evening Shift - No. 10)
Let $\vec{a}$ and $\vec{b}$ be two vectors, Let $|\vec{a}|=1,|\vec{b}|=4$ and $\vec{a} \cdot \vec{b}=2$. If $\vec{c}=(2 \vec{a} \times \vec{b})-3 \vec{b}$, then the value of $\vec{b} \cdot \vec{c}$ is :
$-48$
$-60$
$-84$
$-24$
Explanation
$$\overrightarrow b .\overrightarrow c = \overrightarrow b .(2\overline a \times \overrightarrow b ) - 3\overline b .\overrightarrow b $$
$$ = 0 - 3|\overline b {|^2} = - 48$$
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