Question

if [A bar +B bar]=[A bar - B bar] find the angle between A and B​

Answer 1

Answer:

A+B=A-B

=|A+B| =|A-B|

By parallelogram law of vectors

A²+B²+ 2ab cos∅=A²+ B²-2ab cos∅

=4AB cos∅=0

=cos∅=0°

=∅=π2

Answer 2

Given :

representing bar of P as : P'

[A' +B']=[A' - B']

To Find :

Angle between A & B.

Step-by-step explanation:

Taking square on both sides :

$[A' +B']^2 = [A' - B']^2\\\\|A'|^2 + |B'|^2 + 2A'.B'cos(\theta) = |A'|^2 + |B'|^2+2A'.B'cos(\theta)$

On simplifying ,

$4A'.B'cos(\theta) = 0\\\\A'.B'cos(\theta) = 0\\\\cos(\theta) = 0 \\ \theta = \pi n$

where n is odd

Hence ,

the Angle between A vector and B vector according to given condition :

$\pi n$

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