Definition and Notation A vector is a quantity that has both size (magnitude) and a direction. What is a vector? When do vectors occur? velocity (direction and speed), force, acceleration, weight This vector could be written as: Notation A a a The magnitude (size) is written as: O

Vectors in column form c a 8 from x 4 from y Write each of the following in column form. d b

Multiplying by a scalar Magnitude of a vector The magnitude is the vectors size (length) regardless of direction. 3a a a Find the magnitude of b. Leave your answer as a surd. b

Unit vectors b A unit vector has a magnitude of 1 unit. Check this has one unit: Consider the vector a from the last slide. 3 4 To find the unit vector of a simply divide the x and y components by the magnitude. Find the unit vector of b shown below. b

Vector addition and subtraction 1 Consider the following two vectors: Using the column form b a b a 2 How can we represent the red line shown? 8 a+b How can we represent the red line shown? p a+b q How can we represent the red line shown? -p+q =p-q

Vector addition and subtraction 2 The diagram below shows a parallelogram, OABC, where O is the origin. OA is represented by vector a and OC by vector c. c) The position vector of B. Position vector starts at the origin, O. OB = OA + AB OB = a + c d) AC AC = AO + OC AC = -a + c AC = c - a Given that M is the midpoint of AB find, e) AM Using only vectors a and c find the following: a) AB c parallel to OC f) The position vector of M. b) BC -a parallel to AO