Unit 2 - Objective 3 - Vector Addition by Components
Quick Review

A vector, v, in the x-y plane with components vx and vy can be represented as an ordered pair.

 v = (vx , vy) where the x-component is 1st and the y-component is 2nd.

Length of v = Magnitude of v = |v| =

Direction of v = where tan =

Addition and scalar multiplication of vectors in a plane.

We have represented and added vectors geometrically as arrows. Now we will add vectors algebraically.

Definition: Let A = (a1 , a2) and B = (b1 , b2)       then:
 A + B = (a1 + b1 , a2 + b2) Add corresponding components. cA = c(a1 , a2) = (ca1 , ca2) A constant, c, times a vector multiplieseach component by c.

Example 1

Given A = (2,-5) and B = (7,8), find each of the following:

1) A + B = (2 + 7 , -5 + 8) = (9,3)

2) 3A = 3(2,-5) = (6,-15)

3) 3A - 2B = 3(2,-5) - 2(7,8) = (6,-15) + (-14,-16) = (-8,-31)

4) |A| =     = 5.385

A vector, v, in space can be represented as an ordered triple.
 v = (vx , vy , vz) where the x-component is 1st, the y-component is 2nd, and the z-component is 3rd. Also: (v1 , v2 , v3)

Length of v = Magnitude of v = |v| =

Example 2

Find |v| for v = (1,-2,3)