Question

if |A + B| = |A| = |B|, then the angle between A and B is? (Vectors) (Irrelevant answers will be reported)

Answer 1

Answer:

120°

Explanation:

|A+B|=|A|=|B|=|R| (let's suppose)

then,

we know,

|A+B|²=|A|²+|B|²+2|A||B|cos #

where # is the angle between vectors A and B.

=>|R|²=|R|²+|R|²+2|R||R| cos #

=>|R|²=2|R|²+2|R|² cos #

=>|R|²=2|R|²(1+ cos #)

if R is not a null vector.then,|R|≠0,so

=>1/2=(1+cos #)

=>cos #=-1/2

thus,#=120° as (0≤#≤180°)

Answer 2

Explanation:

Let the angle is a.

so ..

lA+Bl^2 = lal^2 + lBl^2 +2|A||Bl cosa

or..

x^2 =x^2 +x^2 +2x^2cosa

or

cos a=-1/2

or

a=120°