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

Following are solutions to the given points:

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a. It is meaningless.

b. It has meaning.

c. It has meaning.

d. It has meaning.

e. It is meaningless.

f. It is meaningless.

Step-by-step explanation:

a. (a.b).c.

This is meaningless, a.b will give a scalar and we can't take the dot product of the scalar result with vector c.

b. (a.b)c

This has meaning, a.b will give a scalar, the the scalar will be multiply with the vector c.

c. |a|(b.c)

This has meaning, |a| means magnitude of vector a and it will a scalar and this is multiple by the scalar result of b.c

d. a.(b+c)

This has meaning, b+c will give another vector then, the scalar product of the result and vector c will be calculated and it will gives us a scalar answer.

e. a.b+ c

This is meaningless, the dot product of a.b will give a scalar result and the scalar result canont be added to c. We can't add a scalar to a vector.

f. |a|.(a+b)

This is meaningless, |a| means the magnitude of vector a and that is a scalar. The scalar product of a scalar and a vector cannot be calculated.

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