Define a vector and give two examples.

A quantity with magnitude and direction, for example force and displacement.

What is the difference between distance and displacement?

Distance is the total path length (scalar); displacement is the straight-line change in position with direction (vector).

How are two vectors added in a scale drawing?

Tip to tail; the resultant joins the start of the first to the end of the last.

State the parallelogram rule.

Draw both vectors from one point and complete the parallelogram; the diagonal from that point is the resultant.

What is the resultant of two perpendicular vectors a and b?

Magnitude √(a² + b²) at angle θ to a, where tan θ = b/a.

What are the components of a force F at angle θ above the horizontal?

Horizontal F cos θ; vertical F sin θ.

Why does a larger angle to the horizontal reduce the horizontal component of a force?

Because cos θ decreases as θ increases from 0° to 90°.

What are the components of weight W on a slope of angle θ?

W sin θ down the slope and W cos θ perpendicular to it.

How do you find the resultant of vectors that are not at right angles by calculation?

Resolve each into perpendicular components, add the components in each direction, then use Pythagoras and tan θ.

Why can a circular lap have zero average velocity but non-zero average speed?

The displacement is zero but the distance travelled is not.

What accuracy tips improve a scale drawing?

A large scale, sharp pencil, protractor and ruler read without parallax, and a labelled scale.

How is a vector subtracted?

Add its reverse: a − b = a + (−b).

Scalars, vectors and resolvingEdexcel A-Level Physics: Flashcards

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Define a scalar and give two examples.

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Define a scalar and give two examples.: A quantity with magnitude only, for example speed and mass.
Define a vector and give two examples.: A quantity with magnitude and direction, for example force and displacement.
What is the difference between distance and displacement?: Distance is the total path length (scalar); displacement is the straight-line change in position with direction (vector).
How are two vectors added in a scale drawing?: Tip to tail; the resultant joins the start of the first to the end of the last.
State the parallelogram rule.: Draw both vectors from one point and complete the parallelogram; the diagonal from that point is the resultant.
What is the resultant of two perpendicular vectors a and b?: Magnitude √(a² + b²) at angle θ to a, where tan θ = b/a.
What are the components of a force F at angle θ above the horizontal?: Horizontal F cos θ; vertical F sin θ.
Why does a larger angle to the horizontal reduce the horizontal component of a force?: Because cos θ decreases as θ increases from 0° to 90°.
What are the components of weight W on a slope of angle θ?: W sin θ down the slope and W cos θ perpendicular to it.
How do you find the resultant of vectors that are not at right angles by calculation?: Resolve each into perpendicular components, add the components in each direction, then use Pythagoras and tan θ.
Why can a circular lap have zero average velocity but non-zero average speed?: The displacement is zero but the distance travelled is not.
What accuracy tips improve a scale drawing?: A large scale, sharp pencil, protractor and ruler read without parallax, and a labelled scale.
How is a vector subtracted?: Add its reverse: a − b = a + (−b).

Exam questions on Scalars, vectors and resolving

A hiker walks 6.0 km due east and then 8.0 km due north, taking 3.0 hours in total.
Determine the bearing of the hiker's final position from the starting point.2 marks
A child pulls a sledge across level snow using a rope. The tension in the rope is 60 N and the rope makes an angle of 35° above the horizontal.
Calculate the vertical component of the tension in the original situation and state its direction.2 marks
A boat crosses a river 120 m wide. Its engine gives it a velocity of 3.0 m s⁻¹ relative to the water, directed at right angles to the banks. The water flows at 1.5 m s⁻¹ parallel to the banks.
Calculate the magnitude and direction of the boat's resultant velocity relative to the river bank.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).