The meaning of vectors

Represent magnitude and direction and identify equal vectors at different positions.

Meaning

A vector has magnitude and direction and can be represented in a plane by an arrow or components. A scalar, such as temperature or mass, is represented by one number.

Example

A displacement of 3 m east and 4 m north has components and magnitude 5 m. Moving the starting point can still represent the same displacement vector.The straight displacement is the hypotenuse with legs 3 m and 4 m, so its magnitude is √(3²+4²)=5 m. This differs from the 7 m traveled along the two legs.Magnitude differs from path length. Traveling 3 m east then 4 m north covers 7 m, but the displacement magnitude is 5 m.

Practice for this concept

Scope and references

Topics

Magnitude and direction, vectors and scalars, equal vectors

Learning goal

Represent magnitude and direction and identify equal vectors at different positions.

Helpful background

Explore directions, travel distances, and coordinates.

Distance traveled and displacement

Does not ask you to calculate component operations or dot products directly.

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