Formulas and Vector Equations

I'm bored, so I thought I'd get started a little early :)

Distance: Square root of (x2-x1)^2 + (y2-y1)^2 + (z2+z1)^2

Midpoint: (x1+x2/2  y1+y2/2  z2+z1/2

Sphere: (x-xo)^2 + (y-yo)^2 + (z-zo)^2 = r^2

Vector Equation: (x,y,z) = (xo,yo,zo) + t(a,b,c)

Parametric: x= xo+at  y=yo+bt  z=zo+ct

Magnitude of U = square root of a^2+b^2+c^2

EXAMPLE1: With the give points, find the vector equation and parametric (2,3) (0,1)

(2,3) + (0,1)

= (2,4)

(x,y)= (2,3) + t(2,4) 

x= 2 + 2t

y= 3 + 4t

step 1: Add the points to find your vector

step 2: Plug your first given point and your new vector straight into the formula

step 3: x= the x value of your first given point and the a value of the new vector with t behind it

step 4: y= the y value of your first given point and the b value of the new vector with t behind it 

EXAMPLE2: Find the magnitude of u (3,4)

square root of 3^2 + 4^2

= square root of 9 + 16

= square root of 25

=5

step 1: plug given points into your magnitude formula (square root of x^2 + y^2)

step 2: 3x3 + 4x4

step 3: after you multiply, then add, you are going to get 25

step 4: square root 25 to get your final answer of 5

EXAMPLE 3: Find a vector equation of the line through A(3,4) & B(5,5)

(3,4) + (5,5) = (8,9)

(x,y)= (3,4) + t(8,9)

Step1: Add points to find vector.

Step2: Plug your first given point and your new vector directly into the formula