First slide

Motion in a plane

Question

The resultant of two vectors $\large \Vec P$ and $\large \Vec Q$ is $\large \Vec R$ .If the magnitude of $\large \Vec Q$ is doubled, the new resultant becomes perpendicular to $\large \Vec P$ ,then the magnitude of $\large \Vec R$ is

Moderate

A

P² - Q / 2PQ
B

P+Q / P-Q
C

Q
D

P/Q

Solution

Tan 90⁰ = 2Qsinθ/(P+2Qcosθ) ( $∴$ magnitude is doubled)
⇒
$\infty =\frac{2Qsin\theta}{P+2Qcos\theta}\Rightarrow P+2Qcos\theta=0$
$R=\sqrt{P^2+Q^2+2PQcos\theta}$
$=\sqrt{Q^2+P(P+2Qcos\theta)}=\sqrt{Q^2} \Rightarrow R=Q$

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