Vectors

This past week we learned about vectors.

A vector is the same as a slope. Here are the steps to solving certain vector equations:

1)Vector addition: v+u = + =
2)Vector subtraction: v-u = - =
3)Scalar multiplication: kv = k =
4)To find a vector from two points: P2 - P1
5)Vector equation: (x,y) = (x0,y0) + t(a,b)
6)Parameter equations: x = x0 +at y = y0 + bt
7) /v/ = square root of x^2 + y^2 :this equation finds the magnitude of a vector

Example: Give the component form of AB and find /AB/. A (4,7) B(3,2)

P2 - P1: (3, 2) - (4, 7) = (3-4, 2-7) = <-1, -5>

square root of -1^2 + -5^2
= square root of 1+25
= square root of 26

Example 2: Find vector of OP and give its component form

P(6, 72 degrees)
x/6 = cos50
x = 6 cos 72
x = 1.854

y/6 = sin72
y = 6 sin 72
y = 5.706

<1.854, 5.706>

Example 3: u = (6,4) v = (-1,9)
u + v
<6 + -1, 4 + 9> = <5, 13>