Question

Given vectors A= (Axi + Ayj), B= (Byj+Bzk) and C= (Cyj + Czk).

a) find the triple product of these vectors defined by A dot (BxC) in terms of the vector components.

I get 0 as the answer.

b) is the result found in a) a scalar of a vector?

since I had to multiply finally by the scalar product, the answer in a is scalar.

Am I right?

Well, looking at BxC, jxj is zero, jxz is i, kxj is minus i, and kxk is zero.
BxC is By*Cz (i) + Bz x Cy (-i)

Dotting that with Axi hardly gives zero. Check my work, I did it in my head.

dot products always gives scalars.