NOTE:

a, b, and c are to be regarded as vectors

Please regard '*' as the dot for multiplication, too.

Question 1:

a * b * c

When I see this, I am unaware how to approach it. Should I tackle it left to right as I would normally?

a * b will yield a scalar value using the dot product. Then if I take the result and * c, I will have a scalar multiple times a vector. So the result is a vector?

OR do I do a1*b1*c1 + a2*b2*c2 + a3*b3*c3 and the result is a scalar?

Question 2:

(a * b) * c

I would naturally attack the brackets first of all and the resulting value will be scalar. Then continuing on, I have a scalar result value times the vector c. So, the final result is a scalar multiple of vector c, correct?