Question

if a is equal to 2 b and R is equal to b then angle between a and b is equal to​

Answer 1

Answer...

|a + b |^2= a^2 + 2 a.b + b^2 = |a |^2= a^2.

Therefore , 2 a.b + b^2 = 0.

But, |a | = | b |. Therefore,

2b^2 cos ( theta ) + b^2 = 0. Therefore ,

cos (theta)= -(1/2) or

(theta) = 120 degree.

Note that ( theta ) is angle between vectors a and b.

Another method...

Vector A , B and A+B have the same magnitude a= b

=A+B have the same direction and magnitude as the the diagonal of a parallelogram formed by A and B, ( see figure)

=mag(A+B)= a^2+b^2+2.a.b.cos(alpha)

=where alpha is the angle formed by A and B

=replace mag(A+B)= mag(A)=mag(b)= a we will get

=cos(alpha)= -1/2

=so alpha= 120 degrees