// Numbas version: finer_feedback_settings
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Given vectors $\\boldsymbol{v}$ and $\\boldsymbol{w}$, find their inner product.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "You are given the vectors $v= \\var{vector(a,b,g)}$ and $w = \\var{vector(c,d,f)}$ in $\\mathbb{R}^3$.
", "advice": "\\begin{align}
\\langle v,w\\rangle =v^T \\cdot w &= \\begin{pmatrix}\\var{a} &\\var{b} & \\var{g}\\end{pmatrix} \\begin{pmatrix}\\var{c}\\\\\\var{d}\\\\\\var{f}\\end{pmatrix} \\\\
&= \\simplify[timesdot]{{a}*{c}+{b}*{d}+{g}*{f}} \\\\
&= \\var{inner}
\\end{align}
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