Question

What is the angle between A and the resultant of (A+ 2B) and (2A - 2B ) ?

Answer 1

Answer:

|A+B| = |A-B|

Square both sides:

|A+B|^2 = |A-B|^2

The magnitude of a vector V is the square root of the dot product with itself, i.e.

|V| = sqrt(V*V), so:

(A+B)*(A+B) = (A-B)*(A-B)

A*A + 2A*B + B*B = A*A - 2A*B + B*B

or 2A*B = -2A*B

Thus, A*B = 0, making the angle between them 90 degrees.