Question

How to tell if a vector is positive or negative?

Answer 1

Determine if a vector is positive or negative, one must choose a positive direction and use this as a reference to assign signs to vectors. Positive vectors point in the chosen direction, while negative vectors point in the opposite direction.

Step-by-step explanation:

To determine whether a vector is positive or negative, you undertake the following steps:

1. Choose a positive direction. For example, in a scenario involving motion east and west, if west is chosen as the positive direction, then movement towards the east is considered negative.
   
   
2. Add or subtract the magnitudes of the vectors, using the designated signs based on step 1.
   
   
3. The direction of the resultant vector should be stated in words, as in whether the result is positive (in the chosen positive direction) or negative (in the opposite direction).

A vector in one-dimensional motion can be labeled positive or negative depending on its direction relative to the chosen coordinate system.


For example, if the upward direction is taken as positive, a force acting downwards is a negative vector.

Remember to remain consistent with the direction you choose. If you select rightward motion as positive, positive vectors point right and negative vectors point left. This consistency is important when assessing the direction of vectors such as displacement, velocity, and acceleration.