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nid404:
Prove that if (c-a).b=0 and (c-b).a=0 and (b-a).c=0. SHow that this can be used to prove the following geometrical results.
a) The lines through the vertices of the triangle ABC perpendicular to the opposite sides meet in a point.
b) If the tetrahedron AOBC has two pairs of perpendicular opposite edges, the third pair of edges is perpendicular.

Prove also that , in both cases OA2+BC2=OB2+CA2=OC2+AB2

Please help...

astarmathsandphysics:
I will try and do it before i in out but am with a student now.

nid404:

--- Quote from: astarmathsandphysics on November 19, 2009, 02:22:08 pm ---I will try and do it before i in out but am with a student now.

--- End quote ---

ohkay...plz do it before tom...I have a test...I understand the question but don't know how to answer it

Thanks :)

astarmathsandphysics:
Prove that if (c-a).b=0 and (c-b).a=0 and (b-a).c=0. SHow that this can be used to prove the following geometrical results.
a) The lines through the vertices of the triangle ABC perpendicular to the opposite sides meet in a point.
b) If the tetrahedron AOBC has two pairs of perpendicular opposite edges, the third pair of edges is perpendicular.

Prove also that , in both cases OA2+BC2=OB2+CA2=OC2+AB2

Please help...
(c-a).b=cb-ab=0(1)
(c-b).a=ca-ba=0(2)
(1)-(2) gives cb-ab -ca+ba=cb-ca-ab+ba= c.(b-a)-ab+ba=0
the dot product has irrelevant order so u.v=v.u so above becomes  (b-a).c-ab+ab=(b-a).c0

astarmathsandphysics:
look at these

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