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Find the subraction of vector A and B a...

Find the subraction of vector A and B as shown in the figure , also find the direction of subtraction vector ,Given A=4 unit and b=3 unit .

A

`=sqrt(19)unit ` `60`

B

`=sqrt(24)unit ` `45^(@)`

C

`=sqrt(17)unit ` `46.1^(@)`

D

`=sqrt(13)unit ` `46.1^(@)`

Text Solution

Verified by Experts

The correct Answer is:
D
According to the question ,we draw the following figure .

Resultant of the vectors A and B
`r=sqrt(A^(2)+B^(2)-2AB costheta)`
`=sqrt(16+9-2xx4xx3 cos60^(@))`
`=sqrt(13)unit `
` "and direction of the subtraction vector"`
`tanalpha=(bsintheta)/(A-Bdcostheta)=(3sin60^(@))/(4-3costheta)=1.04`
`alpha =tan ^(-1) (1.04)=46.1^(@)`
thus A-B is `sqrt(13)` unit at `46.1^(@)` from A in the dirrection shown in figure.
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