If the angle between A and B is 60° Then the
value of A + B is √x and A - B is √y. Find the
value of x + y.
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When the angle between A and B is 60,
A+B = √x
A-B = √y
From the parallelogram law of vector addition, we know that
A+B = √(A²+B²+2ABcosθ)
√x = √(A²+B²+2ABcos60)
x = A²+B²+2AB*1/2
x = A²+B²+AB
Similarly,
A-B = √(A²+B²-2ABcosθ)
√y = √(A²+B²-2AB*cos60)
y = A²+B²-2AB*1/2
y = A²+B²-AB
Therefore,
x+y = A²+B²+AB+A²+B²-AB
x+y = 2A²+2B² = 2(A²+B²)
Hope this is helpful to you
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