Representing Vectors as Diagrams (Edexcel IGCSE Maths)

Vector Diagrams

Spec point — 6.1C

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

  • $a$ 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 $\overset{\rightarrow}{AB}$

  • Here the arrow will point toward B
  • Vector $\overset{\rightarrow}{BA}$ 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 $a+b$

  • Draw the vector $a$
  • Draw the vector $b$ starting at the endpoint of $a$
  • Draw a line that starts at the start of $a$ and ends at the end of $b$

• To draw the vector $a-b$

  • Draw the vector $a$
  • Draw the vector $-b$ starting at the endpoint of $a$
  • Draw a line that starts at the start of $a$ and ends at the end of $-b$