parameterfremstillingen:
42
( x, y, z ) =
43
( 2+1s-3t, 5-1s-7t, -1+1s+4t )
44
Angiv en parameterfremstilling
45
for den normal til α, der går
46
gennem punktet A ( 8, 7, -4 )
47
Hjælp:
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Planen α er bestemt ved
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punktet Q ( 2, 5, -1 ) samt to
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vektorer u = [ 1, -1, 1 ] og v =
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[ -3, -7, 4 ], der udspænder
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planen, som har
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parameterfremstillingen:
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OP = OQ + s u + t v, s, t ∈ R.
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En normalvektor til planen er
56
krydsvektoren n = u × v. Vi
57
søger en parameterfremstilling
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for den linie, der er vinkelret på
59
α, og som går gennem punktet
60
A ( 8, 7, -4 ). Planens
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normalvektor anvendes som
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retningsvektor for linjen, hvis
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parameterfremstilling dermed
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er givet ved
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OS = OA + u · n, u ∈ R.
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Normalvektoren n's koordinat-
67
sæt beregnes og indsættes
68
i parameterfremstillingen.
69
70
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