Prove that vector A .vector B = vector B .vector A .

Question

Prove that \(\vec A.\vec B=\vec B. \vec A\).

Answer 1

Let θ is the angle between \(\vec A\) and \(\vec B\).

∴ \(\vec A.\vec B=AB\,cos\,\theta\)    ...(i)

and \(\vec B.\vec A=BA\,cos\,\theta\)  ...(ii)

from eqn. (i) and (ii),

\(\vec A.\vec B=\vec B.\vec A\)