The Spontaneous Dot Product

 Today's lesson is on the Dot Product.

First here are some key notes you need to know about the dot product

• If the dot product equals zero, then the vectors are orthogonal, which means perpendicular. If the vectors are multiples of each other, then they are parallel. 
• When finding the angle between two vectors, use the formula: cos(theta)= u*v/magnitudeU * magnitudeV

Now how do we find the dot product:

• First you have two points.
• To find the product of something means to multiply.
• u*v= (x1)(x2)+(y1)(y2) is the dot product formula.

Properties of the Dot Product:

• 1.  commutative: u * v = v * u
• 2.  squared: u * u = magnitude of u^2 
• 3.  K(u * v)= Ku * v does not distribute. "I had problems with this on my test LOL."
• 4.  u * (v+w) = u * v + u * w

Examples:

• Find (3,2) * (5,-4): 3(5)+2(-4) =7
• Find (3/4,2/4) * (1/2,-5/2): 3/4(1/2)+2/4/(-5/2) =0 =orthogonal
• Find the value of (a) if the vectors (12,a) and (6,3) are parallel. a/4=6/8 6a=12 divide both sides by 8 a=3

That's the basics of the Dot product.