Scalars & Vectors (AQA A-Level Mathematics): Flashcards

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Scalars & Vectors
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Definition of a scalar

A quantity with magnitude only, no direction

Definition of a vector

A quantity with both magnitude and direction

Examples of scalar quantities

Speed, distance, time, mass

Examples of vector quantities

Velocity, displacement, force, acceleration

What does the length of a vector arrow represent?

The magnitude of the vector

Graphical method to add vectors

Place vectors head-to-tail, draw resultant from tail to head

Definition of resultant vector

Vector representing combined effect of two or more vectors

Effect of scalar multiplication on a vector

Changes magnitude but not direction

Formula for resultant magnitude using Pythagoras

R=A2+B2R = \sqrt{A^2 + B^2}

Formula to find direction angle of resultant

tan⁡θ=oppositeadjacent\tan \theta = \frac{\text{opposite}}{\text{adjacent}}

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