If $|\bar{a}|=\sqrt{26},|\bar{b}|=7$ and $|\bar{a} imes \bar{b}|=35$, then $\bar{a} \cdot \bar{b}$ is-

Question

If $|\bar{a}|=\sqrt{26},|\bar{b}|=7$ and $|\bar{a} 	imes \bar{b}|=35$, then $\bar{a} \cdot \bar{b}$ is-

Aicharya · Accepted Answer

$\begin{aligned} & \because|\vec{a} 	imes \vec{b}|=|\vec{a}||\vec{b}| \sin 	heta \ & \Rightarrow 35=\sqrt{26} 	imes 7 	imes \sin 	heta \ & \Rightarrow \sin 	heta=\frac{5}{\sqrt{26}} \ & \Rightarrow \cos 	heta=\frac{1}{\sqrt{26}}\end{aligned}$ Now, $\vec{a} \cdot \vec{b}=|\vec{a}||\vec{b}| \cos 	heta$ $\begin{aligned} & =\sqrt{26} 	imes 7 	imes \frac{1}{\sqrt{26}} \ & =7\end{aligned}$

If $|\bar{a}|=\sqrt{26},|\bar{b}|=7$ and $|\bar{a} \times \bar{b}|=35$, then $\bar{a} \cdot \bar{b}$ is-

Solution