Question

If |A vector +B vector|=|A vector|=|B vector|,then the angle between A vector and B vector is

Answer 1

Given that ..

magnitude of A+B vectors =magnitude of A vector=magnitude of B vector=say x.

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°

Answer 2

Given:  |A vector +B vector|=|A vector|=|B vector|

To Find: The angle between A vector and B vector

Solution:

Let A vector be a, B vector be b, and C vector be the resultant of a and b

Let be the angle between the vectors a and b

|c| = √(a² + b² + 2abcosθ)

c = a = b = x                             ....Given

x = √(x² + x² + 2x²cosθ)

On squaring both sides

x² = 2x² + 2x²cosθ

x² - 2x² = 2x²cosθ

-x² = 2x²cosθ

-1/2 = cosθ

cos 120 = -1/2                           (From Standard trigonometric tables)

θ = 120°

Therefore, the angle between a vector and b vector is  120°.