Imagine trying to push a broken-down car while your friend pushes from a slightly different angle — where does the car actually go? To answer this, physicists use scale vector diagrams to map out complex forces. Forces are vectors, meaning they have both a magnitude (size) and a specific direction.
In a vector diagram, forces are represented by straight arrows. The length of the arrow represents the magnitude of the force according to a set scale, and the arrowhead points in the direction the force acts.
In the Higher Tier paper, you must draw accurate scale diagrams to find a resultant force, which is a single force that has the exact same effect as all the original forces acting together.
You must choose a sensible, simple scale, such as or . Your drawing should be large enough to fill at least half the available space to improve precision. Examiners are extremely strict with accuracy: lines must be precise to within and angles to within .
Always use a sharp HB pencil, a ruler, and a protractor. Never rub out your construction lines, as they prove your method to the examiner.
There are two main geometric methods to find the resultant of two forces.
The parallelogram of forces method is used when two forces act from the exact same starting point (tail-to-tail). You draw dashed lines parallel to each vector to form a four-sided shape, then draw the resultant force as the solid diagonal line originating from the starting point.
The tip-to-tail method (or triangle method) is used when you place the tail of the second vector at the tip of the first. The resultant is the straight line drawn directly from the start of the very first vector to the end of the final vector.
Two forces, and , act on an object at an angle of to each other. Describe how to find the resultant force.
Step 1: Choose a sensible scale.
Step 2: Draw the original forces tail-to-tail.
Step 3: Construct the parallelogram.
Step 4: Draw and measure the resultant.
Instead of combining forces together, you can do the exact reverse by resolving a force. This is the process of splitting a single diagonal force into two perpendicular parts, known as components (usually horizontal and vertical).
To resolve a force graphically, draw the original force to scale at the correct angle. Then, form a right-angled triangle around it by dropping vertical and horizontal lines from the tip down to the axes. Measure the lengths of these horizontal and vertical sides and use your scale to convert them back into newtons.
Alternatively, you can calculate the components mathematically using trigonometry. If a force acts at an angle to the horizontal, the components are:
An object is in equilibrium when the resultant force acting on it is exactly zero. According to Newton's First Law, an object in a state of equilibrium will either be perfectly stationary or moving at a constant velocity in a straight line.
In a vector diagram, equilibrium is represented by a closed loop. If you draw all the forces acting on an object tip-to-tail, the tip of the final arrow will perfectly meet the exact starting tail of the first arrow, forming a completely closed shape (like a triangle for three forces).
Students often choose awkward scales like 1 cm = 3 N or 7 N to fit the page, but this leads to calculation errors; always stick to simple scales like 1 cm = 1 N or 1 cm = 10 N.
In 4-mark vector drawing questions, examiners expect to see your dashed construction lines; never erase them, as they act as your 'working out'.
Ensure your pencil is extremely sharp, as Edexcel mark schemes penalise lines that are off by more than ±1 mm or angles incorrect by more than ±2°.
When asked for a direction, provide it as a precise angle relative to a specific axis (e.g., '30° from the horizontal') or as a three-digit bearing (e.g., 045°).
Magnitude
The size or numerical value of a physical quantity, such as the length of a vector arrow representing the size of a force.
Resultant force
A single force that has the exact same effect on an object as all the original forces acting together.
Parallelogram of forces
A graphical method of adding two vectors by placing them tail-to-tail and completing a four-sided figure where opposite sides are parallel.
Tip-to-tail
A geometric method of adding vectors by connecting the end of one vector arrow to the beginning of the next.
Resolving a force
The process of splitting a single force into two perpendicular components that have the same overall effect.
Components
The two perpendicular forces (usually horizontal and vertical) that a single angled force is split into.
Equilibrium
A physical state where the resultant force on an object is zero, resulting in the object being stationary or moving at a constant velocity.
Closed loop
The visual representation of equilibrium in a vector diagram, where drawing all forces tip-to-tail creates a fully enclosed geometric shape with no gaps.
Put your knowledge into practice — try past paper questions for Physics
Magnitude
The size or numerical value of a physical quantity, such as the length of a vector arrow representing the size of a force.
Resultant force
A single force that has the exact same effect on an object as all the original forces acting together.
Parallelogram of forces
A graphical method of adding two vectors by placing them tail-to-tail and completing a four-sided figure where opposite sides are parallel.
Tip-to-tail
A geometric method of adding vectors by connecting the end of one vector arrow to the beginning of the next.
Resolving a force
The process of splitting a single force into two perpendicular components that have the same overall effect.
Components
The two perpendicular forces (usually horizontal and vertical) that a single angled force is split into.
Equilibrium
A physical state where the resultant force on an object is zero, resulting in the object being stationary or moving at a constant velocity.
Closed loop
The visual representation of equilibrium in a vector diagram, where drawing all forces tip-to-tail creates a fully enclosed geometric shape with no gaps.