Maximum and minimum magnitudes of the resulta | vedclass

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(A) The maximum magnitude of the resultant of two vectors $P$ and $Q$ is given by $R_{max} = P + Q$.The minimum magnitude of the resultant of two vect

Vedclass · Accepted Answer

$P = 2Q$

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(A) The maximum magnitude of the resultant of two vectors $P$ and $Q$ is given by $R_{max} = P + Q$.The minimum magnitude of the resultant of two vectors $P$ and $Q$ is given by $R_{min} = |P - Q|$.According to the problem,the ratio of the maximum to the minimum magnitude is $3:1$,so $\frac{P + Q}{P - Q} = \frac{3}{1}$.By cross-multiplying,we get $P + Q = 3(P - Q)$.Expanding the equation,we have $P + Q = 3P - 3Q$.Rearranging the terms,we get $4Q = 2P$,which simplifies to $P = 2Q$.

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

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