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phy131studiof16:lectures:chapter3a [2016/07/28 13:31]
mdawber [Vectors - Multiplication by a scalar]
phy131studiof16:lectures:chapter3a [2016/07/28 13:39] (current)
mdawber [Vectors - Multiplication by a scalar]
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 Multiplication of a vector by a scalar can change the magnitude, but not the direction of the vector, ie. each component of the vector is multiplied by the scalar in the same way. Multiplication of a vector by a scalar can change the magnitude, but not the direction of the vector, ie. each component of the vector is multiplied by the scalar in the same way.
 +
 +===== Unit Vectors =====
 +
 +{{unitvectors.png}}
 +
 +It can be useful to express vector quantities in terms of [[http://​en.wikipedia.org/​wiki/​Unit_vector|unit vectors]]. These are dimensionless vectors of length = 1 that point along the coordinate axes. They are usually denoted with carets (hats), i.e. $(\hat{i},​\hat{j},​\hat{k})$
 +
 +For example:
 +
 +$\vec{v}\,​\mathrm{ms^{-1}}=v_{x}\,​\mathrm{ms^{-1}}\,​\hat{i}+v_{y}\,​\mathrm{ms^{-1}}\,​\hat{j}+v_{z}\,​\mathrm{ms^{-1}}\,​\hat{k}$
 +
 +or
 +
 +$\vec{r}\,​\mathrm{m}=x\,​\mathrm{m}\,​\hat{i}+y\,​\mathrm{m}\,​\hat{j}+z\,​\mathrm{m}\,​\hat{k}$
  
 ===== Vectors and motion ===== ===== Vectors and motion =====
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