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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^(@)`
`R=sqrt(A^(2)+B^(2)+2AB cos 90^(@))=sqrt(5^(2)+12^(2))=13m`
Let angle of `vecR` from `vecA` is `alpha`
`tan alpha=(B sin theta)/(A+B costheta)=(12 sin 90^(@))/(A+Bcos theta)=(12sin 90^(@))/(5+12cos 90^(@))=(12xx1)/(5+12xx0)=(12)/(5)`
or `alpha=tan^(-1)(12)/(5)` with vector `vecA` or `(alpha+20^(@))` with X-axis
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