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Find vecA + vecB and vecA - vecB in the...

Find `vecA + vecB and vecA - vecB` in the diagram shown in figure. Given A = 4 units and B = 3 units.

Text Solution

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Addition : `R = sqrt(A^2 + B^2 + 2 AB cos theta)`
`sqrt(16 + 9 + 2 xx 4 xx 3 cos 60^(@)) = sqrt(37)` units
`tan alpha = (B sin theta)/(A + B cos theta) = (3 sin 60^(@))/(4 + 3cos 60^@) = 0.472`
`:. alpha = tan^(-1) (0.472) = 25.3^@`
Thus, resultant of `vecA and vecB` is `sqrt(37)` units at angle `25.3^@` from `vecA` in the direction shown in figure.
Subtraction:
`S = sqrt(A^2 + B^2 - 2 AB cos theta)`
`sqrt(16 + 9 - 2 xx 4 xx 3 cos 60^(@))`
`= sqrt(13)` units
and
`tan theta = (B sin theta)/(A - B cos theta)`
`= (3 sin 60^(@))/(4 - 3cos 60^@) = 1.04`
`:. alpha = tan^(-1) (1.04) = 46.1^@`
Thus, resultant of `vecA and vecB` is `sqrt(13)` units at `46.1^@` from `vecA` in the direction shown in figure.
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