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A vector vecA and vecB make angles of 20...

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

Text Solution

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