Maximum and minimum magnitudes of the resultant of two vectors of magnitudes P and Q are found to be in the ratio 3:1 . Which of the following relations is true

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Maximum and minimum magnitudes of the resultant of two vectors of magnitudes P and Q are found to be in the ratio $3 : 1$ . Which of the following relations is true

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P = Q

P = 2 Q

P = 4 Q

P = Q/3

answer is B.

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Detailed Solution

\frac{P + Q}{P - Q} = \frac{3}{1}

$P + Q = 3 (P - Q)$

$P + Q = 3 P - 3 Q$

$Q + 3 Q = 3 P - P$

$4Q = 2 P$

$\frac{4}{2} = \frac{P}{Q}$

$\frac{2}{1} = \frac{P}{Q}$

$P : Q = 2 : 1$

$P = 2 Q$

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