MAS5146 Lecture 1 Notes

• Two directed line segments PQ and RS are said to be equivalent if PQ and RS have the same length and are parallel
• A vector is defined to be a collection of equivalent directed line segments
• The word scalar is used as a synonym for a number
• Let A and B be two vectors then A = B iff they have the same length and direction
• The sum of the two vectors A and B is the vector A+B formed when the initial point of A is joined to the terminal point of B when the initial
  1. A+B = B+A
  2. A + (B+C) = (A+B)+C

Notation: A - B = A +(-B)
|A| denotes the magnitude of the vector A

1. |A| > 0 with |A| = 0 iff A = 0
2. |A+B| <= |A| + |B|

If s is a scalar and A is a vector then sA is the vector having magnitude |s||A| and having the same direction as S if s > 0 and the opposite direction if s < 0.sA is called a scalar multiple of A

1. 0A = 0
2. 1A = A
3. (-1)A = -A
4. (s+t)A = sA + tA
5. s(A+B) = sA + sB
6. s(tA) = stA

A vector whose magnitude is 1 is called a unit vector

Let i + j represent the unit vectors parallel to the x and y axis and in the positive direction.