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Chapter Summary

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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 \(\vec{R}_y=R\sin(\theta)\).