1. Warm up
1.) (3, 2, -4), (-1, 0, -7)
Find the vector in standard position and find the magnitude of the vector.

2. 8.4: Perpendicular Vectors

3. Inner Product of Vectors in a Plane
If a and b are 2 vectors (a1, a2), (b1, b2):
Then the inner product of a and b is defined as:
a ● b = a1∙b1 + a2∙b2
This is also called the dot product
Two vectors are perpendicular iff the dot product = 0
Examples: a= (3, 12), b = (8, -2) c = (3, -2)
1.) a ● b 2.) b ● c

4. Inner product of vectors in space
If a and b are 2 vectors (a1, a2,a3) (b1, b2, b3):
Then the inner product of a and b is defined as:
a ● b = a1∙b1 + a2∙b2 + a3∙b3
Examples: a= (3, 12, 5), b = (8, -2, -4)
1.) a ● b

5. Cross Product Given a = (a1, a2, a3) and b = (b1, b2, b3) then:
Then the cross product a x b is given by:
Example: a = (5, 2, 3), b = (-2, 5, 0)