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.