Proof and vectors

• Disproof by counter-example: the easiest way to prove a mathematical statement is false. Just find one example where the statement doesnt hold.
• Proof by deduction: Use known facts to build up your argument and show a statement must be true.
• Proof by exhaustion: break things down into 2 or more cases. Make sure your cases cover all possible situations, then prove separately that the statement is true for each case.
• There are 3 main types of proof:

  • disproof by counter-example
  • proof by deduction
  • proof by exhaustion
• A scalar only has magnitude.
• A vector has magnitude and direction.
• Vectors are parallel when they are scalar multiples of each other.
• If you add two vectors together, you get the resultant.
• A vector that starts from the origin is called a position vector.
• A unit vector is any vector that has a magnitude of 1.
• The magnitude of a vector is its size and is written as |r|.
• The direction of a vector is usually measured by the angle you turn anticlockwise from the positive x axis.