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The resultant of vectors vecP and vecQ is vecR. The resultant becomes 2vecR when vecP is either doubled or reversed in V its direction. |
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Answer» The value of P : Q is `sqrt(3) : sqrt(5)` When P is reversed one gets `P^(2)+Q^(2)-2PQ cos theta= 4R^(2)` From eqn (i) and (ii) one get `-4PQ cos theta=3R^(3)implies PQ cos theta=-(3)/(4) R^(2)` When P is doubled , `4P^(2)+Q^(2)+4PQ cos theta=4R^(2)` `4P^(2)+4Q^(2)-8PQ cos theta= 16R^(2)` `(4 xx`eqn. (ii)) From eqn. (iii) and (iv) `(3Q^(2)-12PQ cos theta= 12R^(2)` `3Q^(2)=12R^(2)+12PQcostheta=12R^(2)+12(-(3)/(4))R^(2)` `=12R^(2)-9R^(2)=3R^(2)` `:. Q= R` Substituting in eqn (i) `P^(2) +R^(2)+2PQ cos theta=R^(2)` `:.P^(2) = -2PQ cos theta=-2 -2(-(3)/(4)R^(2))=(3)/(2)R^(2)implies P=sqrt((3)/(2))`R `:. P: Q = sqrt(3) :sqrt(2)`. |
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