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A vector vec(A) and vec(B) make angles o...

A vector `vec(A)` and `vec(B)` make angles of `20^(@)` and `110^(@)` respectively with the X-axis. The magnitudes of these vectors are `5m` and `12m` respectively. Find their resultant vector.

Text Solution

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Angle between the `vecA and vecB = 110^(@) - 20^(@) = 90^(@)`
So `R= sqrt(A^(2) + B^(2)+ 2AB cos 90^(@))= sqrt(5^(2) 12^(2))= 13m `
Let angle of `vecR` from `vecA` is `alpha`
`tanalpha = (Bsintheta )/(A+B sin theta)= (12sin 90^(@))/(5+12 cos 90^(@))= (12xx1)/(5+12xx0) = (12)/(5)`
`rArr alpha = tan^(-1) ((12)/(5))` with vector `vecA or (alpha + 20^(@))` with X-axis.
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