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If the angle between \( \vec{a} \) and \( \vec{b} \) is \( \frac{2 \Pi}{3} \) and the projection of \( \vec{a} \) in the direction of \( \vec{b} \) is \( -2 \), then \( \mid \) a
\( 1= \)
Options:
\( 1= \)
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1154 Upvotes
Verified Answer
The correct answer is:
\( 04 \)
(C)
\[
\begin{array}{l}
\theta=\frac{2 \pi}{3} \\
\Rightarrow \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}=-2 \\
\Rightarrow \frac{|\vec{a}||\vec{b}| \cos \theta}{|\vec{b}|}=-2 \Rightarrow|\vec{a}| \cos \frac{2 \Pi}{3}=-2 \Rightarrow|\vec{a}| \times-\frac{1}{2}=-2 \Rightarrow|\vec{a}|=4
\end{array}
\]
\[
\begin{array}{l}
\theta=\frac{2 \pi}{3} \\
\Rightarrow \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}=-2 \\
\Rightarrow \frac{|\vec{a}||\vec{b}| \cos \theta}{|\vec{b}|}=-2 \Rightarrow|\vec{a}| \cos \frac{2 \Pi}{3}=-2 \Rightarrow|\vec{a}| \times-\frac{1}{2}=-2 \Rightarrow|\vec{a}|=4
\end{array}
\]
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