Math Help - Three vectors lie in a plane

1. Three vectors lie in a plane

Can i just find the triple scalar product a.(b x c)

And if it = 0 then it lies in the plane?

Can i just find the triple scalar product a.(b x c) = 0 then it lies in the plane?
Yes this is true for three non-zero vectors.

3. Originally Posted by Plato
Yes this is true for three non-zero vectors.
Thanks

So for v1 = (−2, 2, 0), v2 = (6, 1, 4) and v3 = (2, 0,−4)

The cross product is 58

4. I don't understand what you are doing.

$v_1\cdot(v_2\times v_3)=72$

5. Originally Posted by Plato
I don't understand what you are doing.

$v_1\cdot(v_2\times v_3)=72$
Yeah i did something wrong, i used this to help me thanks

6. A short cut for the triple product is this:
If $v_1= $, $v_2= $, and [tex]v_3= <x_3, y_3, z_3> then the cross product is the determinant:
$v_1\cdot(v_2\times v_3)= \left|\begin{array}{ccc}x_1 & y_1 & z_1 \\ x_2 & y_2 & z_2 \\ x_3 & y_3 & z_3 \end{array}\right|$