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The resultant of two vectors vec(P) and ...

The resultant of two vectors `vec(P)` and `vec(Q)` is `vec(R)`. If `vec(Q)` is doubled then the new resultant vector is perpendicular to `vec(P)`. Then magnitude of `vec(R)` is :-

A

P

B

`(P+Q)`

C

Q

D

`(P-Q)`

Text Solution

Verified by Experts

The correct Answer is:
C
(c ) We have `2Q sintheta=P,as RbotP`

Now,R`sqrt(P^(2)+Q^(2)+2PQcos(90^(@)+theta))`
`=sqrt(P^(2)+Q^(2)-2PQsintheta)`
`=sqrt((2Qsintheta)^(2)+Q^(2)-2(2Qsin theta)Qsintheta)`
`=sqrt(4Q^(2)sin^(2)theta+Q^(2)-4Q^(2)-4Q^(2)sin^(2)theta)`
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