Vectors - Which of the following do not make sense?

a) u . (v + w)


b) (u . w) ||w||


c) ||u|| . (v + w)


d) (u + v)w





I'm confused on exactly what I should be looking for. Any help would be greatly appreciated. I know that two vectors become a number (u . v) = # so anything like (u . v) . u doesn't make since, but other than that is there something I should look for?

Vectors - Which of the following do not make sense?
a) u . (v + w)


v+w is a vector


and therefore you can take dot product of 2 vectors


b) (u . w) ||w||


this also makes sense, the dot product of u and w give you a number which can be multiplied by the number ||w||


c) ||u|| . (v + w)


this one does not make sense, since the only way to take a dot product is of 2 vectors, and ||u||is a number not a vector


d) (u + v)w this one does not make sense since u+v is NOT a number, but a vector
Reply:In (d) you have the sum of two vectors multiplying a third vector (w), but what kind of multiplication is it?





If it was (u+v).w it would be ok, since (u+v) is a vector and we can then use the dot product with another vector w. But


what (d) is showing is one vector (u+v)


'times' another vector. But we can't multiply vectors this way.