# Differences

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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] Both sides previous revision Previous revision 2016/07/28 13:39 mdawber [Vectors - Multiplication by a scalar] 2016/07/28 13:31 mdawber [Vectors - Multiplication by a scalar] 2016/07/28 13:30 mdawber [Vectors - Components] 2016/07/28 13:29 mdawber 2016/07/28 13:28 mdawber created 2016/07/28 13:39 mdawber [Vectors - Multiplication by a scalar] 2016/07/28 13:31 mdawber [Vectors - Multiplication by a scalar] 2016/07/28 13:30 mdawber [Vectors - Components] 2016/07/28 13:29 mdawber 2016/07/28 13:28 mdawber created Line 41: Line 41: 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 ===== 