Which of the following expressions are meaningfull operations ?

Options

A. `vec(u) . (vec (v)xx vec(w))`
B. `(vec(u) . vec(v)) .(w)`
C. ` (vec(u).vec(v)) vec(w)`
D. ` vec(u) xx (vec(v).vec(w))`

Answer

A, C

Explanation

` (a) vec(u) .(vec(v) xx vec(w))` is a meaningful operation .
Therefore (a) is the answer.
`(b) vec(u) . (vec(v) ". " vec(w))` is not meaningful since `vec(v) ". " vec(w) ` is a scalar quantity and and for the dot product both quantities should be vectors
Therefore (b) is the not hte answer .
`(b) (vec(u) ". " vec(v)) vec(w)` is meaningful since it is a simple multplication of vectors and scalar quantity. Therefore (c) is the answer .
(b) `vec(u) xx (vec(v) ". " vec(w))` is not meaningful , since `vec(v) "." vec(w) ` is a scalar quantity and for cross product both quantities should be vectors
Therefore (d) is the not the answer.