Question

Which of the following expressions are meaningful? Which are meaningless? Explain. (a) (a · b) · c (a · b) · c has ---Select--- because it is the dot product of ---Select--- . (b) (a · b)c (a · b)c has ---Select--- because it is a scalar multiple of ---Select--- . (c) |a|(b · c) |a|(b · c) has ---Select--- because it is the product of ---Select--- . (d) a · (b + c) a · (b + c) has ---Select--- because it is the dot product of ---Select--- . (e) a · b + c a · b + c has ---Select--- because it is the sum of ---Select--- . (f) |a| · (b + c) |a| · (b + c) has ---Select--- because it is the dot product of ---Select--- .

Answer 1

(a) (a · b) · c has Meaningless because it is the dot product of two scalars.

(b) (a · b)c has Meaningful because it is a scalar multiple of a scalar and a vector .

(c) |a|(b · c) has Meaningful because it is the product of two scalars .

(d) a · (b + c) has Meaningful because it is the dot product of two vectors .

(e) a · b + c has Meaningless because it is the sum of a scalar and a vector.

(f) |a| · (b + c) has Meaningless because it is the dot product of a scalar and a vector .