Question

Can the magnitude of a vector have a negative value? Explain.

Answer 1

Vectors can be positive or negative, and a negative vector points in the opposite direction to the reference positive direction.

Step-by-step explanation:

Just like scalars which can have positive or negative values, vectors can also be positive or negative. A negative vector is a vector which points in the direction opposite to the reference positive direction. For example, if in a particular situation, we define the upward direction as the reference positive direction, then a force F₁ = 30 N downwards would be a negative vector and could also be written as F₁ = -30 N. In this case, the negative (-) sign indicates that the direction of F₁ is opposite to that of the reference positive direction.

Answer 2

The magnitude of a vector is the square root of its components squared. When you square a negative number, you will always get a positive number. Its like speed of your car. It will always be positive (or 0) whether you are moving forward or you are in reverse gear or stationary.