Vectors?!?!?

Question

Given: a − b = c and c = h54, 36i.
Which of the following expressions is NOT
meaningful?
1. (c · a) − |b|
2. a · (b · c)
3. (c · a)b
4. c · (a + b)
5. 20(c · a)b

Thanks for looking. I am not exactly sure what is meant by "meaningless" any help would be appreciated.

Answer 1

Meaningless means that the operation is not defined in a vector space.

1. c*a = the dot product of two vectors is a number; the magnitude of a vector is also a number, so 1 is defined.
2. The dot product only exist between vector...you cannot take a dot product of a vector and a number...meets the meaningless criteria.
3. The scalar multiplication exist...product is defined.
4. dot product of the vector c and the vector resulting from the sum of a+b is defined.
5. And, from all of the above, 5 is a defined quality.

Your job know is to make the appropriate substitutions and solve. Good luck.

Answer 2

a, b, and c are all vectors.

2. a · (b · c) is not meaningful.
(b . c) is a scalar. So you can't take the dot product of a vector a and a scalar. A dot product is between two vectors.