6.2a.notebook
March 14, 2012
1. Find the components of the vector with direction angle 100o and magnitude of 4.
Dot Product of Vectors
Dot Product of u and v:
Properties
1. 2.
3.
4.
5.
1
6.2a.notebook
March 14, 2012
Find each dot product:
1. u =
and v =
2. Use dot product to find length.
3. u =
4.
2
6.2a.notebook
March 14, 2012
Angle Between Two Vectors
If θ is the angle between the nonzero vectors u and v, then
Found by using law of cosines.
v ­ u
v
u
1. Find the angle between the vectors .
u = and v =
3
6.2a.notebook
March 14, 2012
Orthogonal and Parallel Vectors
2 vectors are orthogonal(almost same as perpendicular) if and only if
(except for the zero vector...it is orthogonal to
every vector but not perpendicular)
2 vectors are parallel if u = kv, for some constant
k.
Practice:
1. Find the angle between the vectors
(i + 3j) and (2i ­ 2j).
2. Are these vectors orthogonal?Parallel?Neither?
a)
b)
4
6.2a.notebook
March 14, 2012
Journal: How do you find the dot product
of u and v?
5