A vector quantity may be represented by an arrow. The length of the arrow…

The idea

A vector quantity has both magnitude and direction, unlike a scalar which has magnitude only. To represent a vector, draw a straight arrow: its length is proportional to the magnitude, using a stated scale, and its orientation shows the direction. For example, a 20 N force acting horizontally to the right could be drawn as a 4 cm arrow using the scale 1 cm = 5 N. Changing the scale changes the drawn length but not the physical vector. When several vectors act, each is drawn tip-to-tail at the correct angle, allowing a resultant to be found. Always state the scale and use a ruler and protractor so the drawing is accurate.

What earns the marks

• State that a vector has both magnitude and direction, whereas a scalar has magnitude only.
• Explain that the arrow's length is proportional to the magnitude and must be drawn using a stated scale.
• Explain that the arrow's direction, including its orientation and sense, represents the direction of the vector quantity.
• Use a ruler and protractor to draw a vector accurately, and label the scale and the quantity represented.
• Interpret a given arrow diagram by reading its length against the scale and its direction from a stated reference line.

Common mistakes and how to put them right

• Treating length alone as the vector.

  Put it right: The arrow must also show direction, so always include an arrowhead and orientation.

• Forgetting to state or apply a scale.

  Put it right: Without a scale, the drawn length cannot be converted to a magnitude.

• Drawing the arrowhead at the wrong end or reversing the sense.

  Put it right: The arrowhead shows the direction in which the vector acts.

Exam tips

• Write the scale next to the diagram, for example 1 cm = 5 N, before drawing any arrow.
• Measure length from the tail to the tip of the arrowhead, not to the middle of the arrowhead.
• When comparing vectors, refer to both magnitude and direction rather than length alone.