Vector Negative, Vector Difference - Theorem 2

Figure 10.1.12: Vector negative

We next define the vector negative, -A, and the vector difference, B - A. If A is the vector from P to Q, then -A is the vector from Q to P (Figure 10.1.12). B - A is the vector which, when added to A, gives B; i.e.,

A + (B - A) = B.

Thus if A is the vector from P to Q and B is the vector from P to R, then B - A is the vector from Q to R (Figure 10.1.13).

Figure 10.1.13: Vector difference

If a trader initially has a commodity vector A and sells a quantity b₁ of the first commodity and b₂ of the second, his new commodity vector will be the vector difference A - B.

Given a force vector F, -F is the force vector of the same magnitude but exactly the opposite direction.

If an object initially has position vector P, then Q - P is the displacement vector which will change its position to Q.

Rule(iv) is illustrated in Figure 10.1.14.

Figure 10.1.14