The resultant of two vectors P and Q is R.If Q is doubled then the new resultant vector is perpendicular to P.Then R is equal to?

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dk_ch Share
Sep 21, 2017

drawn

Let the angle between two vectors #P and Q # be #alpha# and their resultant is #R#

So we can write

#R^2=P^2+Q^2+2PQcosalpha......[1]#

When Q is doubled then let the resultant vector be #R_1#, So we can write

#R_1^2=P^2+4Q^2+4PQcosalpha......[2]#

Again by the given condition #R_1# is perpendicular to #P#

So #4Q^2=P^2+R_1^2......[3]#

Combining [2] and [3] we get

#R_1^2=P^2+P^2+R_1^2+4PQcosalpha#

#=>2PQcosalpha=-P^2......[4]#

combining [1] and [4] we get

#R^2=P^2+Q^2-P^2#

#=>R=Q#

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