Vectors • Vectors are quantities that are described by a direction and a magnitude (size or distance denoted with absolute value). • Vectors are primarly used in physics. For example, vectors are used for velocity of a plane, a person swimming across a river or a person walking on a moving train.

Addition of Vectors • Given represents the motion of a object 15 units south from A to B, and represents the movement of the object 10 units southeast, we say that is the vector sum of and. A 15 B 10 C

Visually • **NOTE: order is irrelevant when adding vectors A 15 B 10 C

Subtraction of Vectors • A negative vector is the same length, but in the opposite direction. -v v

Vectors can be added as well as subtracted. • Find v – w given: [this also means v + (-w) ] v w v v-w -w

Ex. 1: ABCD is a square. Complete each statement. D C 4 A B a) b) c) d) e)

Multiplication of Vectors v + v = 2 v

Ex. 2: • Make a diagram that illustrates a force of 8 N north and a force of 6 N west acting on a body. Illustrate the resultant sum of these 2 forces. Find its strength and determine the direction (W of N) of the force.

Ex. 3: • An airplane has a velocity of 400 mi/h southwest. A 50 mi/h wind is blowing from the west. Find the resultant speed and direction of the plane.

Ex. 4: • Vectors t and r are given. Sketch a) 3 r + 2 t and b) r – 2 t -t r - 2 t r r t t r r r t 3 r + 2 t -t