Calculus 3: 12.3Dotproduct

Answer and show work.

1. If is the angle between 2,0,3 and 5,1,2, then

cos()=

2. Assume that uv=9, u=10, and v=1.

What is the value of 6u(8u4v)?

3. A triangle is defined by the three points:

A=(10,8)

B=(2,5)

C=(5,10)

Determine all three angles in the triangle (in radians).

a=

b=

c =

4. The projection of u=3,1,3 along v=1 ,0,2 is

u||=

5. If u=5,0,0 and v=1,3,1 then

the component of u along v is

6. Let a=5,1,1 and b=2,5, 5, then find the decomposition a=a||+a of a with respect to b

a||=

a=