Vectors

A vector is a slope.

vector addition: v+u=+=

vector subtraction: v-u= -=

vector multiplication: kv=k=

To find a vector from two points:

p2-p1

Vector equation:

(x,y)=(x0, y0)+t(a,b)

Parametic equations:

x=x0+at

y=y0+bt

absolute value of v= square root of x^2+y^2= magnitude of a vector

Example 1:

Give the component form of Ab and find the magnitude of AB when 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

Example 2:

Let u= (3,1) and v= (-8,4). Find u+v.

(3+-8, 1+4)

=(-5,5)

Example 3:

Let u= (3,1) v= (-8,4) and w= (-6,-2). Calculate each expression.

a. u+v

(3+-8, 1+4)

=<-5,5)

b. u-v

<3+8, 1-4>

=<11,-3>

c. 3u+w

<9,3> + <-6,-2>

=<3,1>