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# Success in Maths and Science unlocks opportunities

## 1.4 Chapter summary (ESBKF)

Presentation: 23FX

• 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 head-to-tail method or the tail-to-tail method.

• A closed vector diagram is a set of vectors drawn on the Cartesian using the tail-to-head 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 $$\vec{R}_y=R\sin(\theta)$$.