Question
If $|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=7$ and $\vec{\text{a}}\times\vec{\text{b}}=3\hat{\text{i}}+2\hat{\text{j}}+6\hat{\text{k}},$ find the angle between $\vec{\text{a}}$ and $\vec{\text{b}}.$
$=|\vec{\text{a}}|\big|\vec{\text{b}}\big||\sin\theta|.1$ [Since, $\hat{\text{n}}$ is a unit vector]
$\big|\vec{\text{a}}\times\vec{\text{b}}\big|=|\vec{\text{a}}|\big|\vec{\text{b}}\big|\sin\theta\dots(2)$ Given that, $\big|\vec{\text{a}}\times\vec{\text{b}}\big|=\vec{\text{a}}.\vec{\text{b}}$ $|\vec{\text{a}}|\big|\vec{\text{b}}\big|\sin\theta=|\vec{\text{a}}|.\big|\vec{\text{b}}\big|\cos\theta$ $\sin\theta=\cos\theta$ $\theta=\frac{\pi}{4}$ Angle between $\vec{\text{a}}$ and $\vec{\text{b}}=\frac{\pi}{4}$Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$\frac{\text{dy}}{\text{dx}}+\frac{\cos\text{x}\sin\text{y}}{\cos\text{y}}=0$