Calculus – Vectors

Here we only consider vectors in \(\mathbb{R}^3\) (or \(\mathbb{R}^2\)) and use the following notations:

\(\mathbf{v}=\langle v_1,v_2,v_3 \rangle\) is a vector in \(\mathbb{R}^3\).

Also used is \(\mathbf{v}=v_1\,\mathbf{i}+v_2\,\mathbf{j}+v_3\,\mathbf{k}\) with \(\mathbf{i}=\langle 1,0,0 \rangle\), \(\mathbf{j}=\langle 0,1,0 \rangle\) and \(\mathbf{k}=\langle 0,0,1 \rangle\).

\(|\mathbf{v}|=\sqrt{v_1^2+v_2^2+v_3^2}\) is the length or norm of \(\mathbf{v}\).

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Last modified on March 1, 2021