Q93 / 180 · KCET 2019 · Mathematics
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
\( 1= \)
\( 1= \)
- A\( 03 \)
- B\( 11 \)
- Correct answerC\( 04 \)
- D\( 12 \)
Solution
(C)
\[ \begin{array}{l} \theta=\frac{2 \pi}{3} \\ \Rightarrow \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}=-2 \\ \Rightarrow \frac{|\vec{a}||\vec{b}| \cos \theta}{|\vec{b}|}=-2 \Rightarrow|\vec{a}| \cos \frac{2 \Pi}{3}=-2 \Rightarrow|\vec{a}| \times-\frac{1}{2}=-2 \Rightarrow|\vec{a}|=4 \end{array} \]
\[ \begin{array}{l} \theta=\frac{2 \pi}{3} \\ \Rightarrow \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}=-2 \\ \Rightarrow \frac{|\vec{a}||\vec{b}| \cos \theta}{|\vec{b}|}=-2 \Rightarrow|\vec{a}| \cos \frac{2 \Pi}{3}=-2 \Rightarrow|\vec{a}| \times-\frac{1}{2}=-2 \Rightarrow|\vec{a}|=4 \end{array} \]
Hence, the correct answer is option: 'C'.