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Problem:
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Find a number s that garantees that the vectors
i, i+j+k, and i+2j+sk will all be parallel to the
same plane.
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Solution:
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Three vectors are on a plane when and only when they generate
no volume, i.e. their triple scalar product is 0.
Let u,v and w be the three given vectors, |
> u := [1,0,0]: v := [1,1,1]: w := [1,2,s]:
| their triple scalar product is, |
> tsp := dotprod(u,crossprod(v,w));
_
tsp := -2 + s
| s is real (not complex) so its congugate is itself. Hence the value of s that makes tsp = 0 is |
> s = 2: