Math Is Fun Forum

yonski

Member

Registered: 2005-12-14

Posts: 67

Vector question

Hi there, i'm a bit stuck on this question:

" Given 3 non-coplanar vectors a, b and c convince yourself that the position vector r of any point in space may be represented by

r = λa + μb + γc

for some real numbers λ, μ and γ.

Show that

r.(bxc) = λa.(bxc) ,

r.(axb) = γa.(bxc) ,

r.(cxa) = μa.(bxc) . "

I understand how they get the first one - the cross product of b and c  is perpendicular to both of them, so won't contain any b or c components. Hence when you do the dot product you'll be multiplying the b and c bits of r by zero so they disappear. However I don't get the other two...?

Please help!
yonski

Last edited by yonski (2008-10-15 07:40:19)

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Student: "What's a corollary?"
Lecturer: "What's a corollary? It's like when a theorem has a child. And names it corollary."

sce1912

Member

Registered: 2008-10-08

Posts: 5

Re: Vector question

Hi yonski,

For the last 2 you need to use the cyclic symmetry of the scaler triple product (which you may need to prove):
a.(bxc) = b.(cxa) = c.(axb)

Hope this helps

Last edited by sce1912 (2008-10-17 04:10:05)