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Two vectors of 10 units & 5 units make a...

Two vectors of 10 units & 5 units make an angle of `120^(@)` with each other.Find the magnitude & angle of resultant with vector of 10 unit magnitude.

Text Solution

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`|veca + vecb| = sqrt(a^2 + b^2 + 2ab cos theta)`
`= sqrt(100 + 25 + 2 xx 10 xx 5(-1//2)) = 5sqrt(3)`
`tan alpha = (5 sin 120^(@))/(10 + 5 cos 120^(@)) = (5sqrt(3))/(20 - 5) = (5sqrt(3))/(5 xx 3) = 1/(sqrt3)`
`implies alpha = 30^(@)`
[Here shows what is angle between both vectors `120^(@) and "not" 60^@]`
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