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Let AB be a vector in two dimensional pl...

Let AB be a vector in two dimensional plane with the magnitude 4 units and making an angle of `30^(@)` with X-axis and lying in the first quadrant. Find the components of AB along the two axes off coordinates. Hence, represent AB in terms of unit vectors `hati and hatj`.

Text Solution

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Let us consider A as origin. From the diagram, it can be seen that the component off AB along X-axis.

`=1ABcos30^(@)=4cos30^(@)`
`=4xx(sqrt(3))/(2)=2sqrt(3)`
and the component of AB along Y-axis
`=AB sin30^(@)=4xx(1)/(2)=2`
Hence, `AB=2sqrt(3hati)+2hatj`
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