IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: nid404 on November 19, 2009, 02:11:52 pm

Title: :S VECTORS
Post by: nid404 on November 19, 2009, 02:11:52 pm

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...

Title: Re: :S VECTORS
Post by: 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.

Title: Re: :S VECTORS
Post by: nid404 on November 19, 2009, 02:23:15 pm

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.

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

Thanks :)

Title: Re: :S VECTORS
Post by: astarmathsandphysics on November 19, 2009, 11:01:07 pm

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

Title: Re: :S VECTORS
Post by: astarmathsandphysics on November 19, 2009, 11:06:15 pm

look at these

Title: Re: :S VECTORS
Post by: nid404 on November 21, 2009, 06:23:50 am

thank you very much sir  :)