Hey everyone, I have a conceptual question regarding vectors. The question states: Which of the following expressions are well defined for all vectors a, b, c, and d?

A. a * (b x c)

B. magnitude of (a) x (b x c)

C. (a*b) x (c*d)

At first glance, I recognize that (A) is a scalar and that (C) is a cross product of dot products, and (B) and I am not quite sure on (although it appears to be a vector). However, the question is throwing me off. What does it mean to be well defined for all vectors a,b,c, and d? Only (B) appears to be a vector, while (A) and (C) are not. A friend told me that they are all well defined, but I am not sure if he is correct or not. How exactly would I approach this problem?

Any thoughts?

Any feedback appreciated, thanks.