Find the vector sum c = a + b, where a = 3i + 4j + (-1)k and b = 1i + 3j + (-2)k.

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- and z-components:

c = (a_x + b_x)i + (a_y + b_y)j + (a_z + b_z)k

= (3 + 1)i + (4 + 3)j +(-1 + (-2))k

= 4i + 7j -3k