Answer
(a). no meaning, a scalar and a vector
(b). meaning, a vector
(c). meaning, two scalars
(d). meaning, two vectors
(e). no meaning, a scalar and a vector
(f). no meaning, a scalar and a vector
Work Step by Step
Which of the following expressions are meaningful? Which are meaningless? Explain.
(a) (a · b) · c
(a · b) · c has no meaning because it is the dot product of a scalar and a vector.
(b) (a · b)c
(a · b)c has meaning because it is a scalar multiple of a vector .
(c) |a|(b · c)
|a|(b · c) has meaning because it is the product of two scalars .
(d) a · (b + c)
a · (b + c) has meaning because it is the dot product of two vectors .
(e) a · b + c
a · b + c has no meaning because it is the sum of a scalar and a vector.
(f) |a| · (b + c)
|a| · (b + c) has no meaning because it is the dot product of a scalar and a vector.
