Question

what is the angle between A_ and B_ if their resultant is R= squareroot of A²+B²​

Answer 1

Answer:

According to the question,

Resultant = √[ (A+B)² + (A-B)² +2(A+B)(A-B)cosα

= √[ 3A²+B²] …………(1)

Where α is the angle betweenthe two vectors.

Now solving the equation (1)

=> 2(A²+B²) + 2(A² - B²)cosα = 3A²+B²

=> (B²-A²) -2(B²-A²)cosα =0

=> (B²-A²)[ 1- 2cosα] =0

=> either (B²-A²) =0 or (1-2cosα)=0

=> either magnitude(A)= magnitude(B) or α=60°

So your answer is 60°