1. ## 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?

2. ## Re: Find vector C!

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 $\displaystyle (A\cdot B)A-(A\cdot A)B~?$

4. ## Re: Find vector C!

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?

5. ## 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

6. ## Re: Find vector C!

A and C are orthogonal*

7. ## Re: Find vector C!

yes there're
how did you get this formula?!

8. ## Re: Find vector C!

yes they're!!
how did you get this formula?!

9. ## Re: Find vector C!

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 $\displaystyle A$.

10. ## Re: Find vector C!

yes i got it thanks