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 multiplies
each 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)
