Calculus III

  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 Image Upload 1 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 Image Upload 2
  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?
    • Image Upload 3
    • Image Upload 4
  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.  Image Upload 5 also known as the scaler comp

    • 2. Image Upload 6
    • NOTE: may need to sub out Image Upload 7 using DOT product equations.
  8. What is a UNIT Vector?
  9. 1.) Equation of a Sphere?

    2.) Equation of a Ball?
    1. Image Upload 8

    2. Image Upload 9
  10. What is the distance formula for 3D space?
    Image Upload 10
  11. Mid point formula in 3D?
    Image Upload 11
  12. If you are given Point P and point M, what is vector Image Upload 12?
    Image Upload 13 Image Upload 14
  13. Vector Operations?
    Image Upload 15 Vector Addition

    Image Upload 16 Vector Subtraction

    Image Upload 17 Scaler Mult. When C is a constant.
  14. What is the magnitude of a Vector?
    The Length of the vector

    Image Upload 18 is the distance from P to Q therefore mag. is Image Upload 19
Card Set
Calculus III
Calculus III Terms / Equations