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

Options

A. √ 30,√ 22
units
B. √ 40,√ 28
C. √ 37,√ 15
units
D. √
37,√
13

Answer

D

Explanation

`R = sqrt(A^2 + B^2 + 2AB cos theta)`
`=sqrt(16 + 9 +2xx4xx3cos 60^@)`
`=sqrt(37)` units
`tan alpha = (B sin theta)/(A+B cos theta)`
`=(3 sin 60^@)/(4+3 cos 60^@) =0.472`
`:. alpha = tan^(-1) (0.472) = 25.3^(@)`

Thus, resultant of A and B is `sqrt (37)` units at angle `25.3^@` from A in the direction shown in figure.

`S = sqrt(A^2 + B^2 - 2AB cos theta)`
`=sqrt(16+9-2xx4xx3cos 60^(@)) = sqrt13 units`
and `tan alpha = (B sin theta)/(A-B cos theta)`
`= (3 sin 60^@)/(4-3 cos 60^@) = 1.04`
`:. alpha = tan^(-1) (1.04) = 46.1^(@)`
Thus A-B is `sqrt(13)` units at `46.1^@` from A in the direction
Shown in figure.