Vectors and scalars

The idea

A scalar quantity carries magnitude only, so a single number with a unit fully describes it: a mass of 5 kg or a time of 12 s needs nothing more. A vector quantity carries both magnitude and direction, so the description is incomplete until the direction is stated: a force of 20 N acting downwards, or a velocity of 8 m/s due east. The test is whether reversing the direction changes the physical meaning. Reversing a force or a velocity changes what happens to the object, so both are vectors; reversing a mass or an energy value does not, so those are scalars. In multiple-choice questions, compare each option against this two-part test rather than against the length of the wording.

What earns the marks

• States that a scalar quantity has magnitude only, with no direction required.
• States that a vector quantity has both magnitude and direction.
• Applies the test that reversing the direction changes the meaning of a vector but not of a scalar.
• Identifies a named example as scalar or vector and justifies the choice by reference to direction.

Common mistakes and how to put them right

• Treats any quantity with a unit as a vector.

  Put it right: Check instead whether a direction must be stated.

• Assumes that a large magnitude makes a quantity a vector.

  Put it right: Size alone never decides the classification.

• Classifies speed as a vector because it is measured in m/s.

  Put it right: Recognise that velocity, not speed, carries direction.

Exam tips

• Read every option and eliminate those that omit direction from the definition of a vector.
• Ask whether the direction could sensibly be given; if it could and matters, the quantity is a vector.
• Check the wording of the question for the word 'difference' and make sure the chosen option contrasts the two definitions.