Which of the following expressions are meaningful? Which are meaningless? Explain. a) (a\cdot b)\cdot c (a\cdot b)\cdot c has ? because it is the dot

chillywilly12a 2021-05-29 Answered
Which of the following expressions are meaningful? Which are meaningless? Explain.
a) (ab)c
(ab)c has ? because it is the dot product of ?.
b) (ab)c
(ab)c has ? because it is a scalar multiple of ?.
c) |a|(bc)
|a|(bc) has ? because it is the product of ?.
d) a(b+c)
a(b+c) has ? because it is the dot product of ?.
e) ab+c
ab+c has ? because it is the sum of ?.
f) |a|(b+c)
|a|(b+c) has ? because it is the dot product of ?.
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Expert Answer

Clara Reese
Answered 2021-05-30 Author has 120 answers

Step 1
a) The expression (ab)c has meaningless because, it is the dot product of a scalar ab and a vector c.
Note that here, the dot product ab is a scalar, and c is a vector, and a scalar and a vector cannot be dot product with each other.
b) The expression (ab)c has meaningful because, it is a scalar multiple of a scalar ab and the vector c.
Note that here, the dot product ab is a scalar, and c is a vector, and a scalar multiplication is possible with a vector.
c) The expression |a|(bc) has meaningful because, it is the product of two scalars |a| and bc.
Here, two scalars can be multiplied easily.
d) The expression a(b+c) has meaningful because, it is the dot product of two vectors a and b+c.
Note that here, the sum of two vectors, b+c is again a vector, and the two vectors dot product with each other.
e) The expression ab+c has meaningful because, it is the sum of a scalar ab and the vector c.
Note that, a scalar and a vector cannot be added.
f) The expression |a|(b+c) has meaningless because, it is the dot product of a scalar |a| and a vector b+c.
Note that, a scalar and a vector cannot be dot product with each other.

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