The angle of a resultant vector is given by the equation [tex]tan \theta = \frac{R_y}{R_x}[/tex]
Explanation:
When we compute the resultant vector starting from 2 (or more) vectord, we add the components along the x- and y- direction of the original vectors, in order to find the component of the resultant vector along the two directions.
Let's call:
[tex]R_x[/tex] the component of the resultant vector along the x-direction
[tex]R_y[/tex] the component of the resultant vector along the y-direction
The magnitude of the resultant vector is then given by Pythagorean's theorem:
[tex]R=\sqrt{R_x^2+R_y^2}[/tex]
While the angle can be found by taking the arctangent of the ratio between the y-component and the x-component, mathematically:
[tex]tan \theta = \frac{R_y}{R_x}[/tex]
Note that this angle is measured between the resultant vector and the positive direction of the x-axis.
Learn more about vector components:
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