I believe there is a typo in this sentence from a book. Can someeone confirm it?
"Since a.b is a scaler then (a.b)xc has no meaning and a.(bxc) may be wriiten as a.bxc without ambiguity."
I have no idea what "Why do the brackets say nothing?" could mean.
These are vectors. $\displaystyle A\cdot B$ is a scalar, a number.
Cross products are vectors. If $\displaystyle t$ is a scalar and $\displaystyle C$ is a vector then $\displaystyle t\times C$ is meaningless.
A calculator has absolutely nothing to do with vectors.
Taking Plato's example of A= <1, 2, 3> and B= <3, 2, 1>, what does your calculator give for AB or A(B)? There are two kinds of "vector times vector" product (well, three if you include the "exterior product- the exterior product of two n dimension vectors is a n by n tensor.) so the notation "AB" or A(B) is ambiguous.
I get the vector product, -4i, 8j, -4k for AB, A(B) and AxB with the calculator.
I have noticed that with the calculator the scaler product has higher precedence than the vector product which has been confusing me. The vector product has precedence in mathematics. I feel that Casio should fix this with later models.
You are not using that calculator correctly.
Look at this web page.
Look at the dot product.