Vector addition and scale diagrams

≈ 48 min

Vector addition and scale diagrams

A scale vector diagram can communicate direction and relative magnitude, but it must be labelled with a scale, arrows and an order of addition. Add vectors head-to-tail: move the second vector without rotating it so its tail meets the first vector's head. The resultant runs from the tail of the first to the head of the last. For perpendicular components, Pythagoras gives magnitude and trigonometry gives direction. A diagram is an estimate unless a calculation confirms it; when values are supplied, use both the sketch and the numerical method as cross-checks.

Work it through

A displacement of 3 m east followed by 4 m north makes a right triangle. The resultant magnitude is √(3² + 4²) = 5 m. The direction is north of east, with tan θ = 4/3. A response that says only '5 m' is incomplete because displacement is a vector.

Mastery target

Add two vectors graphically and analytically, then report a resultant with magnitude, direction and an interpretable diagram.

In a head-to-tail vector diagram, where does the resultant run?

From the first tail to the final head

From the final tail to the first head only

Around every arrow separately

It has no direction

Name the key physics term from Vector addition and scale diagrams that best fits the explanation and visual model.

A displacement is 3 m east then 4 m north. What is the resultant magnitude in m?

Which statement corrects a common misunderstanding in Vector addition and scale diagrams?

Correct: A resultant is not found by adding magnitudes unless the vectors are along the same line and direction.

A diagram or formula can be used without naming the system, direction or condition.

A measured pattern always proves one cause with no uncertainty or alternative explanation.

Units can be ignored if the numerical answer looks familiar.