Vectors - AS and A2

Letters in bold are vector notations

How do you find a resultant vector?

**a** + **b** or **a** + **b** + **c**

How do you find the **magnitude** of a **3D** vector?

√(**i**^2 + **j**^2 + **k**^2)

How do you find the **angle** between two **3D vectors** (**a** and **b**)?

Draw a triangle, draw a line for (**ab**) find the magnitude of each vector and use the cosine rule

How do I know if the vectors are **parallel**? (2D vectors)

If they have a scalar multiplier applied on their position vector.

What is the **general form** of **parallel** vectors? (2D vectors)

**a** = k**b**

How do you find the **unit vector** (**â**)? (2D vectors)

(1/|**a**|) x **a**

What does **collinear** mean? (2D vectors)

When three or more points pass through the same line

What methods can you use to determine that three points (i.e. A, B and C) are collinear? (2D vectors)

1. Find the vector AB and the vector AC and show that they are parallel by finding a scalar multiplier (a = kb)

2. Find the equation of the line bewtween two points and check that the third point passes through it.

How would you write a 2D vector in **magnitude-direction** form?

(magnitude, direction in degrees)

How would you measure the direction of a 2D vector?

Find the angle the vector makes if you travel anti-clockwise from the x-axis. Always draw a diagram to show to the examiner.