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