# Calculus III

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1. What is a position Vector?
A vector that's tail is at the origin and Head is at some point (V1, V2)
2. What is the Position Vector of points Q(-2,1) and U(6,5)?
The position vector is with the tail at the origin (0,0) and head at (8,4)
3. Find two vectors that are both parallel and 3times the magnitude/length of V. V=<V1,V2>
Two vectors parallel to V are
4. How can a Vector be Orthogonal to another?
Two vectors can be Orthogonal if and only if U⋅V = 0
5. What are the two forms of the DOT product?
6. What are the properties of the DOT Product?
• U⋅V = V⋅U  Commutative property
• C(U⋅V) = (CU)⋅V = U⋅(CV)  Associative property
• U⋅(V+W) = U⋅V+U⋅W  Distributive property
7. 1. If you have projection U onto V (ProjVU) how would you represent the length of the projection?
2. What would the vector created by the projection then be represented by? (Magnitude ⋅ Direction)
1.  also known as the scaler comp

• 2.
• NOTE: may need to sub out  using DOT product equations.
8. What is a UNIT Vector?
9. 1.) Equation of a Sphere?

2.) Equation of a Ball?
1.

2.
10. What is the distance formula for 3D space?
11. Mid point formula in 3D?
12. If you are given Point P and point M, what is vector ?
13. Vector Operations?