1. 12.9 Parallel & Perpendicular Vectors in Two Dimensions

2. If we have cv, it is a scalar multiplied times a vector.
What about a vector times a vector?
Dot Product:
it’s a number!
(not a vector)
Ex 1) Two Truths & a Lie Find the dot product.
A) B) C)
should be 13
Perpendicular vectors have a dot product of 0
called orthogonal vectors.

3. We can utilize the Law of Cosines to find the angle between any two vectors.θ
Ex 2) Find the measure of the angle between vectors

4. Parallel vectors have the same slope, they are scalar multiples of each other.
watch out!
Ex 3) We need to be able to tell if 2 vectors are parallel, perpendicular, or neither using the dot products.
Choose two different options (between , , & N)
Make up 2 questions of your own.
Trade with a partner & solve theirs.

5. Ex 4) Determine the value of K for which each pair of vectors is parallel and the value of K for which they are perpendicular.
Perpendicular:
Parallel:

6. An important application of the dot product in physics is work done on a body through distance.
Work = Force · displacement
(vector) (vector)
Ex 5) Determine the work done by a force of magnitude
(newtons) in moving a box 20 m along a floor that makes an angle of 30° with Give answers in newton-meters (N-m)
(joules = newton-meters)

7. Properties of the Dot Product
Norm
Commutative Property
Distributive Property
Associative Property
Scalar

8. Homework
#1209 Pg #1, 8, 11, 13, 15, 18, 20, 23, 25, 27, 29, 33, 35