Given the scenario: a 45 kg. object is being pushed north with a force of 8n, and at the same time, it is been pushed east with a force of 6n. what will the magnitude and direction be of the resultant vector?

10 N, north-east

Explanation:

The two forces applied on the object are perpendicular to each other, so we can find the magnitude of their resultant by using the Pythagorean theorem:

The direction of the force instead is given by

where F_n is the force pointing north, and F_e is the force pointing east, and the angle is measured with respect to the east direction. Substituting,