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.
Right, the third part is meaningless because you are multiplying two scalars. However, part A and B are both scalars, but the question asks which of the following are well defined for all vectors. Since there are no vectors, I assume it would be none of them.
It is not defined. You can't multiply a scalar x scalar, so it is meaningless I guess.