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→Vector 0
I noticed at the end of calc3.6 that you used <math>\vec{0}</math>. Does this mean a vector with 0 magnitude and direction? Can a vector have direction without magnitude, for that matter? I'd never seen an actual number with the vector sign over it before. [[User:DouglasA|DouglasA]] 20:49, 11 February 2010 (EST)
I noticed at the end of calc3.6 that you used <math>\vec{0}</math>. Does this mean a vector with 0 magnitude and direction? Can a vector have direction without magnitude, for that matter? I'd never seen an actual number with the vector sign over it before. [[User:DouglasA|DouglasA]] 20:49, 11 February 2010 (EST)
:Yes, it's important to remember that when we talk about a vector of zero length, we don't mean just the number 0, which is a number, ie, a member of <math>\mathbb{R}</math>, we mean the ''vector'' <math>\begin{pmatrix}0\\0\\0\end{pmatrix}\in\mathbb{R}^3</math>. Or, in the plane, we may mean <math>\vec{0}\in\mathbb{R}^2</math>. Do you see the difference? [[User:JacobB|JacobB]] 21:39, 11 February 2010 (EST)