Quick Review A vector, v, in the x-y plane with components v_{x} and v_{y} can be represented as an ordered pair.
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.
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.
Length of v = Magnitude of v = |v| = Example 2 Find |v| for v = (1,-2,3) |