Question

What is the angle between (A+B) and (A x B)? Give reason.

Answer 1

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.)

$A\times B=|A||B|sin\alpha n$, where α is the angle between A & B and n is the unit vector perpendicular to the plane containing A & B. So, the angle between $(A+B)$ and $(A\times B)$ is ${90}^0.$

Mathematically,

$|A+B||A\times B|cos\alpha =(A+B).(A\times B)$

$=A.(A\times B)+B.(A\times B)$

$=B.(A\times A)+A.(B\times B)$

$=0+0$