Calculus III

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Author:
gotbordom
ID:
232944
Filename:
Calculus III
Updated:
2013-09-10 00:54:34
Tags:
Calc
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Description:
Calculus III Terms / Equations
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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?
    Vector Addition

    Vector Subtraction

    Scaler Mult. When C is a constant.
  14. What is the magnitude of a Vector?
    The Length of the vector

    is the distance from P to Q therefore mag. is

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