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Question

Resultant of two vectors A and B is of magnitude P. If B is reversed, then resultant is of magnitude Q. What is the value of P2 + Q2 ?

A
2(A2 + B2)
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B
2(A2-B2)
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C
A2-B2
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D
A2 + B2
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Solution

The correct option is B 2(A2 + B2)
Let θ be angle between A and B. Resultant of A and B is
P=A2+B2+2ABcosθ ---(i)

When B is reversed, then the angle between A and - B is (180 - θ).Resultant of A and - B is

Q = A2+B2+2ABcos(180θ)

Q = A2+B2+2ABcosθ --(ii)

Squaring and adding (i) and (ii), we getP2+Q2=2(A2+B2)

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