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What should be the the angle theta betw...

What should be the the angle ` theta` between two vectors `vec A and vec B` for their resultant ` vec R` to be (i) maximum (ii) minimum ? Give their resultant value.

Text Solution

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Magnitude of `overset(rarr)R` is `R=sqrt(A^(2)+B^(2)+2 cos theta`
(i) for R to be maximum `cos theta =+1 or theta =0^(@), R_(max)=sqrt(A^(2)+B^(2)+2AB=(A+B))`
(ii) for R to be minimum `cos theta =-1 or theta =-180^(@), R_(min)=sqrt(A^(2)+B^(2)+2AB(-1)=(A-B)`
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