Verified answer

I assume that i, j, and k are mutually orthogonal unit vectors that form a right-handed coordinate system.

When you do i x j, you get a vector that is perpendicular to both, in the direction determined by the right hand rule. So, that vector is in the same direction as k! (In fact, it is also the same length as k, which means it is equal to k!)

i x j = ak

So, now you've got ak x k, where a is a scalar (and in fact, it's equal to 1), which is the same as

ak x k = a * (k x k)

And we know that any vector crossed with itself gives the zero vector, since the magnitude of the cross product is proportional to the sine of the angle between the vectors. Since the vectors are in the same direction, the angle between them is zero, and sin 0 = 0. So, we have

(i x j) x k = a * 0

which is just the zero vector.

I hope that helps!

Please do re-upload your question in detail. are you trying to get the vector triple cross product by application of tensor? i.e. alternating and substitution tensor? please re ask the question in detail.