Vectors

• What is a vector?

  A series of numbers that represent information such as position, velocity, force etc.
• What are the ways that vectors could be represented?

  • List of numbers
  • Dictionary
  • 1-D array
  • Functions
• What is convex combination of two vectorsequation

  $\left(a\cdot u\right)+$$\left(b\cdot v\right)$

  • u and v are the vectors
  • a+b= 1
  • a and b must be bigger than or equal to 0
• What is convex combination

  a linear combination of points where all co-efficients are non-negative and sum to 1
• What is the dot product and can you plot it on a graph?

  • u . v
  • you can not plot it on a graph as it is a single number
• What is the practical application of the dot product??

  Can be used to find the angle between two vectors
• What is the equation to find the angle theta between two vectors

  • $\frac{A.B}{\left(\left|\left|A\right|\right|.\left|\left|B\right|\right|\right)}$
  • The lengths of A and B are written as ||A|| and ||B||
• What are the steps to calculate angle between two vectors?

  • Calculate the dot products of A and B
  • Calculate the length of vector ||A|| and ||B|| using pythagoras theorem
  • Calculate ||A|| . ||B||
  • Calculate Cos $\theta$
  • Use calculate to find the angle