Question

Question-. (a) Does it make sense to say that a vector is negative? Why? (b) Does it make sense to say that one vector is the negative of another? Why? Does your answer here contradict what you said in part (a)?

Short answer

(a) Yes, it makes sense to say that a vector is negative.

(b) Yes, it makes sense to say that one vector is the negative of another.

Step-by-step solution

Definition

A vector is entities that describe the magnitude as well as the direction of quantity.

Vector tells us about the direction of the entity; if we want to show the opposite direction of any reference vector, then a negative sign is used.

Explanation

Part (a)

A negative vector is a vector that shows its direction with reference to another positive direction vector.

Part (b)

For example, if$\overline{PQ}$is some vector in a particular direction and if we want to show another vector of the same magnitude but in the opposite direction, we will represent it as a negative vector of PQ, i.e.,$-\overline{PQ}$,

$\overline{PQ}=-\overline{PQ}$

Conclusion 

Yes, it is absolutely correct that one vector is negative with respect to the other, as a negative vector defines nothing but direction. If one vector is in the opposite direction to another one, it is said to be a negative vector.