# Find vector C!

• Dec 4th 2011, 12:23 PM
ahmedzoro10
Find vector C!
Given A= [1,1,1] and B=[2,-1,0] Find vector C which is Coplanar With A and B and perpendicular to A My solution:1. The triple product for ll those three vectors should equal 0 (i.e. A.(BXC)= 0)2. A.C=0 (i.e using Dot product)So, I've 2 equations and i can't get C can anybody help, Urgently please?
• Dec 4th 2011, 12:37 PM
Plato
Re: Find vector C!
Quote:

Originally Posted by ahmedzoro10
Given A= [1,1,1] and B=[2,-1,0] Find vector C which is Coplanar With A and B and perpendicular to A

What about $\displaystyle (A\cdot B)A-(A\cdot A)B~?$
• Dec 4th 2011, 12:42 PM
ahmedzoro10
Re: Find vector C!
• Dec 4th 2011, 01:03 PM
Plato
Re: Find vector C!
Quote:

Originally Posted by ahmedzoro10

No. You have to do somethings for yourself.
Have you done those operations.
Is the result coplanar with A & B?
Is it perpendicular to A?
• Dec 4th 2011, 01:11 PM
ahmedzoro10
Re: Find vector C!
I've already 2 equations which consist of x,y and Z for C
First, A, B and C are already coplanar so I got the first equation which is x+2y-3z=0
then, A and C are coplanar so i got the sec. equation which is x+y+z=0
and I can't go on :(
• Dec 4th 2011, 01:15 PM
ahmedzoro10
Re: Find vector C!
A and C are orthogonal*
• Dec 4th 2011, 02:52 PM
ahmedzoro10
Re: Find vector C!
yes there're
how did you get this formula?!
• Dec 4th 2011, 02:53 PM
ahmedzoro10
Re: Find vector C!
yes they're!!
how did you get this formula?!
• Dec 4th 2011, 03:28 PM
Plato
Re: Find vector C!
Quote:

Originally Posted by ahmedzoro10
yes they're!!
how did you get this formula?!

This well known triple vector product:
$\displaystyle A\times(B\times C)=(A\cdot C)B-(A\cdot B)C$.
That is a vector which is coplanar with $\displaystyle B~\&~C$ and is perpendicular to $\displaystyle A$.
• Dec 4th 2011, 03:45 PM
ahmedzoro10
Re: Find vector C!
yes i got it thanks :)