Question

If lA-Bl=lAl-lBl, where A nor B are non-zero vectors, then what is the angle between A and B?

Answer 1

Given:

lA-Bl=lAl-lBl, where A nor B are non-zero vectors

To find:

Angle between A and B

Calculation:

Let angle be $\theta$

$\therefore \: |A - B| = |A| - |B|$

$= > \sqrt{ {A}^{2} + {B}^{2} + 2AB \cos( 180 \degree - \theta) } = A - B$

$= > \sqrt{ {A}^{2} + {B}^{2} - 2AB \cos( \theta) } = A - B$

Squaring on both sides :

$= > {A}^{2} + {B}^{2} - 2AB \cos( \theta) = {A}^{2} + {B}^{2} - 2AB$

Cancelling the common terms:

$= > 2AB \cos( \theta) = 2AB$

$= > \: \cos( \theta) = 1$

$= > \theta = 0 \degree$

Hence final answer is :

Angle between A and B is 0°.