# Thread: three vectors are linearly independent

1. ## three vectors are linearly independent

I am suppose to use the standard volume interpretation of the scalar triple product a dot b crossed with c

where a, b and c are my vectors to support that these vecors are independent. I realize that their determinant matrix is not zero and that is what defines independence, but I do not know what the question is asking me to do!!! Any guidance would be much appreciated. Frostking

2. Originally Posted by Frostking
I am suppose to use the standard volume interpretation of the scalar triple product a dot b crossed with c

where a, b and c are my vectors to support that these vecors are independent. I realize that their determinant matrix is not zero and that is what defines independence, but I do not know what the question is asking me to do!!! Any guidance would be much appreciated. Frostking
If $a\cdot(b\times c)=0$, then the volume of the parallelepiped formed by the three vectors is $0$. But that means that $a$, $b$, and $c$ all lie in the same plane and are therefore not linearly independent. (Since a plane is spanned by exactly two vectors, a third vector in the plane must be a linear combination of the other two.)