Physics - Vectors Question with Solution | TestHub

Given, Two vectors A and B. A and B are two vectors. So, their sum A + B lies in the same plane where A and B lie (Since they are non -parallel so they define a plane and the cross product between them is not zero.) $\mathrm{A}\times \mathrm{B}=|\mathrm{A}||\mathrm{B}|\sin \alpha \mathrm{n}$, where $\alpha$ is the angle between $\mathrm{A}\&\mathrm{B}$ and $\mathrm{n}$ is the unit vector perpendicular to the plane containing A \& B. So, the angle between $(\mathrm{A}+\mathrm{B})$ and $(\mathrm{A}\times \mathrm{B})$ is $90^{\circ }$. Mathematically, $|\mathrm{A}+\mathrm{B}\Vert \mathrm{A}\times \mathrm{B}|\cos \alpha =(\mathrm{A}+\mathrm{B})\cdot (\mathrm{A}\times \mathrm{B})$ $=A\cdot (A\times B)+B\cdot (A\times B)$ $=B\cdot (A\times A)+A\cdot (B\times B)$ $=0+0$