This shows you the differences between two versions of the page.

Both sides previous revision Previous revision | |||

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] |
||
---|---|---|---|

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 ===== |