Question # 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

Vectors
ANSWERED 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 product of ?.
b) $$(a\cdot b)c$$
$$(a\cdot b)c$$ has ? because it is a scalar multiple of ?.
c) $$|a|(b\cdot c)$$
$$|a|(b\cdot c)$$ has ? because it is the product of ?.
d) $$a\cdot(b+c)$$
$$a\cdot(b+c)$$ has ? because it is the dot product of ?.
e) $$a\cdot b+c$$
$$a\cdot b+c$$ has ? because it is the sum of ?.
f) $$|a|\cdot(b+c)$$
$$|a|\cdot(b+c)$$ has ? because it is the dot product of ?. 2021-05-30

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