# 1.1.3 Scalars & Vectors

### What are Scalar & Vector Quantities?

• A scalar is a quantity which only has a magnitude
• A vector is a quantity which has both a magnitude and a direction
• For example, say you go on a hike in the woods to a location which is a couple of miles from your start point
• As the crow flies, your displacement will only be a few miles but the distance you walked will be much longer

Displacement is a vector while distance is a scalar quantity

• Distance is a scalar quantity because it describes how far you have travelled overall, but not the direction
• Displacement is a vector quantity because it tells you how far you are from where you started and in what direction
• The table shows a variety of scalar and vector quantities you will come across in Physics:

Scalars and vectors table

### Combining Vectors

• Vectors are represented by an arrow to indicate its direction and length to represent its magnitude
• We can combine vectors by adding or subtracting them from each other
• There are two methods you can use to combine vectors: the triangle method and the parallelogram method

#### Triangle method

• Step 2: the resultant vector is formed by connecting the tail of the first vector to the head of the second vector

#### Parallelogram method

• Step 1: link the vectors tail-to-tail
• Step 2: complete the resulting parallelogram
• Step 3: the resultant vector is the diagonal of the parallelogram

#### Condition for equilibrium

If three forces acting on an object are in equilibrium, they form a closed triangle

### Resolving Vectors

• A force vector of magnitude F and an angle of θ to the horizontal is shown below

• It is possible to resolve this vector into its horizontal and vertical components

• Fx = Fcosθ
• Fy = Fsinθ
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