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 >

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Ex. 1: Give the component form of Ab and find the magnitude of AB.
A(1,-2), B(3,-2)
(3,-2)-(1,-2)= (3-1,-2+2) = (2,0) vector
square root of -4^2+-3^2= square root of 16+9= square root of 25 = 5 magnitude

Ex.2: Let u= (3,1) and v= (-8,4)

u+v
(3+-8, 1+4)

=(-5,5)