Vector Difference in the Plane:
Find the vector difference d = a - b, where a = 2i - 5j and b = 3i + 2j.
These vectors are shown in the diagram, along with -b, which is a translation and negation of b so that its tail coincides with the head of a. Vector d is drawn from the tail of a to the head of -b, as required by the definition of the vector sum of a and -b.
To find the difference analytically, we subtract the x-components of the vectors to find the x-component of the difference, and do the same for the y-components:
c
= (ax - bx)i + (ay - by)j = (2 - 3)i + (-5 - 2)j = (-1)i + (-7)j = -i - 7j