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1.4 Chapter summary (ESBKF)

A vector has a magnitude and direction.

Vectors can be used to represent many physical quantities that have a magnitude and direction, like forces.

Vectors may be represented as arrows where the length of the arrow indicates the magnitude and the arrowhead indicates the direction of the vector.

Vectors in two dimensions can be drawn on the Cartesian plane.

Vectors can be added graphically using the headtotail method or the tailtotail method.

A closed vector diagram is a set of vectors drawn on the Cartesian using the tailtohead method and that has a resultant with a magnitude of zero.

Vectors can be added algebraically using Pythagoras' theorem or using components.

The direction of a vector can be found using simple trigonometric calculations.

The components of a vector are a series of vectors that, when combined, give the original vector as their resultant.

Components are usually created that align with the Cartesian coordinate axes. For a vector \(\vec{F}\) that makes an angle of \(\theta\) with the positive \(x\)axis the \(x\)component is \(\vec{R}_x=R\cos(\theta)\) and the \(y\)component is \(\vec{R}_y=R\sin(\theta)\).
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