Question

A force vector F1 points due east and has a magnitude of 200N. A second force F2 is added to F1. The resultant of the two vectors has a magnitude of 400N and points along the east/west line. Find the magnitude and direction of F2Source https://www.physicsforums.com/threads/physics-trigonometry.61160/

Answer 1

Answer:

The second vector $\vec{F_2}$ points due West with a magnitude of 600N

Explanation:

The original vector $\vec{F_1}$ points with a magnitude of 200N due east, the Resultant vector $\vec{R}$ points due west (that's how east/west direction can be interpreted, from east to west) with a magnitude of  400N. If we choose East as the positive direction and West as the negative one, we can write the following vectorial equation:

$\vec{F_1}+\vec{F_2}=\vec{R}\implies\vec{F_2}=\vec{R}-\vec{F_1}=-400N-200N=-600N$

With the negative sign signifying that the vector points west.