Representing Vectors as Diagrams (Edexcel IGCSE Maths A: Higher): Revision Note

Vector diagrams

How can I represent a vector visually?

• A vector has both a size (magnitude) and a direction

  • You need to draw a line to show the size of the vector

  • You also need to draw an arrow to show the direction of the vector

• Vectors are written in bold when typed to show that they are a vector and not a scalar

  • When writing a vector in an exam you should underline the letter to show it is a vector

  • $\mathit{a}$ when typed and $\underline{a}$ when handwritten

    • You will not lose marks if you forget to underline vectors

• If a vector starts at A and ends at B we can write it as $\overrightarrow{AB}$

  • Here the arrow will point toward B

  • Vector $\overrightarrow{BA}$ will have the same length but point toward A

What happens when a vector is multiplied by a scalar?

• When you multiply a vector by a positive scalar:

  • The direction stays the same

  • The length of the vector is multiplied by the scalar

• When you multiply a vector by a negative scalar:

  • The direction is reversed

  • The length of the vector is multiplied by the number after the negative sign

What happens vectors are added or subtracted?

• To draw the vector $\mathbf{a}+\mathbf{b}$

  • Draw the vector $\mathbf{a}$

  • Draw the vector $\mathbf{b}$ starting at the endpoint of $\mathbf{a}$

  • Draw a line that starts at the start of $\mathbf{a}$ and ends at the end of $\mathbf{b}$

• To draw the vector $\mathbf{a}-\mathbf{b}$ 

  • Draw the vector $\mathbf{a}$

  • Draw the vector $-\mathbf{b}$  starting at the endpoint of $\mathbf{a}$

  • Draw a line that starts at the start of $\mathbf{a}$  and ends at the end of $-\mathbf{b}$