Scalars and vectors

Physical quantities in the 9702 syllabus are classified as either scalars or vectors.

Scalars

• Have magnitude only and combine by ordinary arithmetic.
• Examples: distance, speed, time, mass, energy, work, temperature, power, density, pressure, charge and potential difference.

Vectors

• Have both magnitude and direction.
• Examples: displacement, velocity, acceleration, force, weight, momentum, electric field strength, gravitational field strength and magnetic flux density.

Combining and resolving vectors

• Vector addition follows the tip-to-tail (head-to-tail) or parallelogram rule, while two perpendicular vectors combine by Pythagoras' theorem.
• Vector subtraction is performed by reversing the direction of the second vector and then adding it.
• Any vector can be replaced by two perpendicular components, taken along a chosen reference axis and perpendicular to it.

$V_{\mathrm{x}}$ = V cos θ (component along the reference axis) $V_{\mathrm{y}}$ = V sin θ (component perpendicular to the reference axis)

These three skills underpin the rest of the AS course: forces in equilibrium (Topic 4), equations of motion in two dimensions (Topic 2), and projectile motion all rely on resolving vectors into independent perpendicular components.

Exam tip Every vector answer must state both magnitude and direction. Always identify whether a given angle is measured from the horizontal or the vertical before applying sin or cos. The component method is the safest route through any multi-vector problem and is the expected technique in exam answers.