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