If $|\bar{a}|=5,|\bar{b}|=13$ and $|\bar{a} imes \bar{b}|=25$. If $\frac{\pi}{2}

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If $|\bar{a}|=5,|\bar{b}|=13$ and $|\bar{a} 	imes \bar{b}|=25$. If $\frac{\pi}{2} < 	heta < \pi$ where $	heta$ is angle between $\bar{a}, \bar{b}$ then $\bar{a} \cdot \bar{b}$ has the value

Aicharya · Accepted Answer

$\begin{aligned} & |\vec{a} 	imes \vec{b}|=|\vec{a} 	imes \vec{b}| \sin 	heta \ & \Rightarrow 25=5 	imes 13 \sin 	heta \ & \Rightarrow \sin 	heta=\frac{5}{13} \ & \Rightarrow \cos 	heta=\frac{-12}{13} \quad\left[\because \frac{\pi}{2} < 	heta < \piight] \ & 	ext { now } \vec{a} \cdot \vec{b}=|\vec{a}||\vec{b}| \cos 	heta=5 	imes 13 	imes \frac{-12}{13}=-60\end{aligned}$

If $|\bar{a}|=5,|\bar{b}|=13$ and $|\bar{a} \times \bar{b}|=25$. If $\frac{\pi}{2} < \theta < \pi$ where…

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