1.1 Scalars & Vectors Scalar & Vector Quantities Scalar quantities have magnitude only. ex. Volume, mass, speed, temperature, distance Vector quantities have magnitude and direction ex. Velocity, acceleration, force, displacement Adding Vectors Vectors are drawn as line segments where the length of the line segment represents the magnitude of the vector and the arrow head represents the direction of the vector. This would represent a displacement vector: p m (East)

1.1 Scalars & Vectors p To add two vectors special care must be paid to the direction of each vector: d 1 = 15 m (E) For example: d 2 = 9 m (E) d 1 + d 2 = 24 m (E) The net or resultant vector when two or more vectors are acting in the same direction would be the simple numerical addition of the vectors.

1.1 Scalars & Vectors p To add these two vectors special care must be paid to the direction of each vector: F 1 = 22 N (South) For example: F 2 = 22 N (North) F 1 + F 2 = 0 N The net force or resultant force in this addition would be zero force. When two or more force acting on a body have a resultant force of zero the body is said to be in equilibrium.

1.1 Scalars & Vectors p In this case two forces, F 1 and F 2, act on a single object in two different directions as shown F1F1 F2F2 F 1 + F 2 = F R The net force or resultant force, F R, in this addition is solved by using rules of adding vectors. F1F1 FRFR The equilibrant, F 3 is a force exactly opposite to the resultant force that is needed to keep an object stationary. F3F3

1.1 Scalars & Vectors p. 6 Another way of looking at adding three vectors: F1F1 F2F2 F 1 + F 2 + F 3 = F R = 0 N The three forces act to keep the object stationary so the sum of the force should be equal to zero F1F1 F3F3 F3F3 ΣF 1 = 0 N

1.1 Scalars & Vectors p. 7 Subtracting Vectors: Method 1: v1v1 v2v2 Δv = v 2 – v 1 It may become necessary to find the difference between two vectors such as finding the change in velocity for a body changing from one velocity, v 1 to second velocity, v 2. Remember that subtracting a vector is just like adding its opposite vector! Δv = v 2 + (-1)v 1 = v2v2 - v 1 v1v1 Δv = v 2 – v 1

1.1 Scalars & Vectors p. 7 Subtracting Vectors: Method 2: v1v1 v2v2 Δv = v 2 – v 1 The difference between two vectors can also be found by drawing vectors “tail to tail”. v 1 + Δv = v 2 Δv = v 2 – v 1 Both method 1 and method 2 will yield the same resultant vector.

1.1 Scalars and Vectors Key Questions In this section, you should understand how to solve the following key questions. Page 5 – Quick Check #1 – 3 Page – Quick Check #1 - 4 Page 10 – Review 1.1: #1 - 4