Lovely Vectors

A vector is a slope.

To find a vector from 2 points: P2-P1

Addition:

v + u =< x, y > + < x1, y1 > = < x+x1, y+y1 >

Scalar Multiplication:

kv= k < x, y > = < kx, ky >

Vector Equation: 

(x,y) = (xo,yo) + t(a,b)

Parametric Equations:

x=xo+at 

y=yo+bt

Magnitude of a Vector:

√(x² + y²)

Component form:

< rcosΘ, rsinΘ >

Ex.1: A force of 4 N acts on angle of 30° with the x-axis find in component form

Your force is r.

< 4cos(30°), 4sin(30°) >

=< 2√(3), 2 >

Ex. 2: Find the vector of (2,1) and (4,0). 

a. Find the vector equation.

b. Express in Parametric form.

Find vector P2-P1 :

(4-2, 0-1) = <2,-1>

a. Using the first point (2,1) and the vector <2,-1>, we can write the equation in the form (x,y) = (xo,yo) + t(a,b)

(x,y) = (2,1) + t(2,-1)

b. Parametric form:

x = 2 + 2t

y = 1 - t

Ex. 3<4,2> - 2<1,-2>

<12,6> - <2,-4>

<10, 10>