Is the Triple Scalar Product Always Zero?

[member 392791]

Hello,

I am confused how vectors that are coplanar will give a triple product of zero? Or is it the case that all 3 vectors must be coplanar for a triple product of zero, or is 2 sufficient? I.e. the vector being dotted with one of the vectors being crossed in the same plane, will this produce a zero scalar product?

 

[D H]

Take any two of those coplanar vectors. The cross product is either zero or is normal to both of those vectors -- and every other vector that is coplanar with those first two vectors. What's the dot product of two vectors that are normal to one another?

 

[member 392791]

ok, so I see that the textbook specified that if all 3 vectors are coplanar, then its triple scalar product is zero, which makes sense to me because the projection is going to be zero. It's just that the accompanying figure 3.28 doesn't make me think that the vectors are coplanar.
EDIT: here is the figure that I am referring to