Question

The angle made by resultant vector R=2underroot3i-2j with x axis is?

Answer 1

Given vector

`vec R=2sqrt3hati-2hatj`

Inspection reveals that resultant has positive value of `x`-coordinate
and `-ve` value of `y`-coordinate. If we draw this vector on a `xy` coordinate system, it lies in the fourth quadrant.

If `theta` is the angle between the vector and the `x`-axis, we have

`tan theta=(-2)/(2sqrt3)`
`=>tan theta=-1/(sqrt3)`
`=>theta=arctan(-1/sqrt3)`
`=>sintheta/costheta=-1/(sqrt3)`

From the unit circle reproduced below we see that for angles in the fourth quadrant we have two values for which we can have `sqrt3`. The first value in the round brackets represents `cos` and second value represents `sin` of particular angle. The required value which gives `sqrt3` in the denominator is

`theta=330^@`