Question

a · (b · c): a. The expression is meaningful. It is a vector. b. The expression is meaningful. It is a scalar. c. The expression is meaningless. The cross product is defined only for two vectors. d. The expression is meaningless. The dot product is defined only for two vectors.

Answer 1

Assuming that a, b and c are all vectors:

The dot product of two vectors
`x\cdot y` returns a number.

Let
`b\cdot c = k`, for some
`k \in \mathbb{R}`

The expression becomes

`a\cdot (b\cdot c) = a\cdot k`

This is the multiplication between a vector and a scalar, and it returns a multiple of the vector.