60 lines
3.3 KiB
Text
60 lines
3.3 KiB
Text
;Related tasks:
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* [[Arrays]]
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* [[Vector]]
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** [[Dot product]]
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** [[Vector products]]
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*** A starting page on Wolfram MathWorld is {{Wolfram|Vector|Multiplication}}.
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*** Wikipedia [[wp:Dot product|dot product]].
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*** Wikipedia [[wp:Cross product|cross product]].
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*** Wikipedia [[wp:Triple product|triple product]].
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*** Wikipedia [[wp:Hodge star operator|hodge star operator]]
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*** Wikipedia [[wp:Inner product space|inner product space]]
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*** Wikipedia [[wp:Outer product|outer product]]
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*** Wikipedia [[wp:Interior product|interior product]]
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*** Wikipedia [[wp:Exterior product|exterior product]]
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*** Wikipedia [[wp:Wedge product|wedge product]]
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*** Wikipedia [[wp:Curry product|curry product]]
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*** Wikipedia [[wp:Pfaffian product|pfaffian product]]
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* [[Matrices]]
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* [[Bivector]]
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* [[Antivector]]
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* [[Tensor]]
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* [[Quaternion]]
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* [[Rotor]]
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* [[Motor]]
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* [[Sedenion]]
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* [[Octonion]]
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<br>
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A vector is defined as having three dimensions as being represented by an ordered collection of '''n''' numbers: i.e. for '''n'''='''3''' : (X, Y, Z).
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If you imagine a graph with the '''x''' and '''y''' axis being at right angles to each other and having a third, '''z''' axis coming out of the page, then a triplet of numbers, (X, Y, Z) would represent a point in the region, and a vector from the origin to the point.
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Given the vectors:
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<big> A = (a<sub>1</sub>, a<sub>2</sub>, a<sub>3</sub>) </big>
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<big> B = (b<sub>1</sub>, b<sub>2</sub>, b<sub>3</sub>) </big>
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<big> C = (c<sub>1</sub>, c<sub>2</sub>, c<sub>3</sub>) </big>
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then the following common vector products are defined:
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* '''The dot product''' (a scalar quantity)
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:::: <big> A • B = a<sub>1</sub>b<sub>1</sub> + a<sub>2</sub>b<sub>2</sub> + a<sub>3</sub>b<sub>3</sub> </big>
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* '''The cross product''' (a vector quantity)
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:::: <big> A x B = (a<sub>2</sub>b<sub>3</sub> - a<sub>3</sub>b<sub>2</sub>, a<sub>3</sub>b<sub>1</sub> - a<sub>1</sub>b<sub>3</sub>, a<sub>1</sub>b<sub>2</sub> - a<sub>2</sub>b<sub>1</sub>) </big>
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* '''The scalar triple product''' (a scalar quantity)
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:::: <big> A • (B x C) </big>
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* '''The vector triple product''' (a vector quantity)
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:::: <big> A x (B x C) </big>
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;Task:
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Given the three vectors:
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a = ( 3, 4, 5)
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b = ( 4, 3, 5)
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c = (-5, -12, -13)
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# Create a named function/subroutine/method to compute the dot product of two vectors.
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# Create a function to compute the cross product of two vectors.
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# Optionally create a function to compute the scalar triple product of three vectors.
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# Optionally create a function to compute the vector triple product of three vectors.
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# Compute and display: <code>a • b</code>
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# Compute and display: <code>a x b</code>
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# Compute and display: <code>a • (b x c)</code>, the scalar triple product.
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# Compute and display: <code>a x (b x c)</code>, the vector triple product.
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