First slide

Motion in a plane

Question

If $\large \overrightarrow P + \overrightarrow Q = \overrightarrow R$ and $\large \overrightarrow P - \overrightarrow Q = \overrightarrow S$ , then R² + S² is equal to

Moderate

A

P² + Q²
B

2(P² - Q²)
C

2(P² + Q²)
D

4 PQ

Solution

$R = \sqrt {{P^2} + {Q^2} + 2PQ\cos \theta } ;S = \sqrt {{P^2} + {Q^2} - 2PQ\cos \theta }$
${R^2} + {S^2} = {P^2} + {Q^2} + 2PQ\cos \theta + {P^2} + {Q^2} - 2PQ\cos \theta = 2({P^2} + {Q^2})$

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