Question

How can we determine the angle of a resultant vector

Answer 1

The angle of a resultant vector is given by the equation $tan \theta = \frac{R_y}{R_x}$

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:

$R_x$ the component of the resultant vector along the x-direction

$R_y$ the component of the resultant vector along the y-direction

The magnitude of the resultant vector is then given by Pythagorean's theorem:

$R=\sqrt{R_x^2+R_y^2}$

While the angle can be found by taking the arctangent of the ratio between the y-component and the x-component, mathematically:

$tan \theta = \frac{R_y}{R_x}$

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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