Representing Vectors as Diagrams (Cambridge (CIE) IGCSE International Maths)

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

  • when typed and  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

  • Here the arrow will point toward B

  • Vector  will have the same length but point toward A

How do I draw a vector on a grid?

• You can draw a vector anywhere on a grid

  • Just make sure it has the correct length and the correct direction

• To draw the vector 

  • Pick a point on the grid and draw a dot there

  • Count 3 units to the right and 4 units up and draw another dot

  • Draw a line between the two dots

  • Put an arrow on the line pointing toward the second dot

• Look out for negatives and zeroes

  •   goes 2 to the right and 4 down

  • goes 2 to the right but does not go up or down

What happens when I multiply a vector 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

• For example,

  • will have the same direction but double the length

  •  will have the same direction but half the length

• 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

• For example, 

  • will be in the opposite direction and its length will be the same

  • will be in the opposite direction and its length will be doubled

What happens when I add or subtract vectors?

• To draw the vector 

  • Draw the vector 

  • Draw the vector  starting at the endpoint of 

  • Draw a line that starts at the start of and ends at the end of 

• To draw the vector  

  • Draw the vector 

  • Draw the vector   starting at the endpoint of 

  • Draw a line that starts at the start of   and ends at the end of