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Line 1: − + − + − + − Alternatively, and often more conveniently, the '''dot product''' of vectors represented by <a,b,c> and <d,e,f> equals a*d + b*e + c*f.+ + + + +
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{{math-h}}
{{math-h}}
The '''dot product''' is defined for two [[Vector|vectors]] X and Y to be:
The '''dot product''' is defined for two [[Vector|vectors]] <math>\vec{X}</math> and <math>\vec{Y}</math> to be:
: <math>X \cdot Y = |X||Y|\cos\theta</math>
: <math>\vec{X} \cdot \vec{Y} = |\vec{X}||\vec{Y}|\cos\theta</math>
where |x| is the norm and theta is the angle between the vectors.
where |\vec{x}| is the norm and <math>\theta</math> is the angle between the vectors.
In 3 dimensional space, for two vectors, <a,b,c> and <d,e,f>, their dot product equals a*d + b*e + c*f.
In n-dimensional space, the dot prodct of two vectors, <math>\vec{v}=(v_1, v_2,...,v_n)</math> and <math>\vec{w}=(w_1,w_2,..., w_n)</math>, is:
:<math> \vec{v}\cdot\vec{w} = v_1w_1 + v_2w_2 +... v_nw_n = \sum_{i=1}^{n}v_iw_i.</math>
Unlike the [[cross product]], the dot product is a [[scalar]], not a vector, and has no direction.
Unlike the [[cross product]], the dot product is a [[scalar]], not a vector, and has no direction.