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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 `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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Knowledge Check

  • The resultant of vec(a) and vec(b) makes alpha with vec(a) and beta with vec(b) , then (a,b represent magnitudes of respective vectors) :

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    B
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    A
    `alpha = tan^(-1)(0.5)`
    B
    `alpha = tan^(-1)(0.6134)`
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