Vectors (Addition and Subtraction)

Vector Addition

The addition of vectors u = 1, u2, u3> = ui+ uj+ uk and v = 1, v2, v3> = vi+ vj+ vk equals the following:

u + v = 1 + v1, u2 + v2, u3 + v3 > = Resultant

Vector Subtraction

The subtraction of vectors u = 1, u2, u3> = ui+ uj+ uk and v = 1, v2, v3> = vi+ vj+ vk equals the following:

u – v = 1 + v1, u2 + v2, u3 + v3 > = Resultant

Graphical Representation of Vector Addition

To add vectors graphically, do the following:

1. Choose either vector and attach the tail of that vector to the head of the other vector.
2. Draw an arrow from the tail of the other vector to the head of the first vector. This is the resultant.

vectors 1

Example 1 – Find the vector addition of u = <1, 2, 3> and v = <4, 5, 6>

u + v = <1+4, 2+5, 3+6> = <5, 7, 9>

Example 2 – Find the resultant of a = 5i + 6j + 7k and b = 8i + 9j -10k.

a + b = (5+ 8)i + (6+ 9) j + (7+ 9)k = 13i + 15j + 17k

Example 3 – Sketch the resultant of vector a and b using the tail-to-head method.

resultant

Take the tail of vector b and attach it to the head of vector a.

graph 1

Draw an arrow from the tail of vector a to the head of vector b. That is the resultant.

graph 2