Hello. I'm currently having some problems on this question on vectors. If you could help me, it'll be great.

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Vector AC is [2,4,-3] and it forms the hypotenuse of a right angled triangle of trangle ABC. Vector AB is parallel to vector [1,1,0]. Find AB.

Well, I've done a little diagram to show you what it looks like. For my working out, I deduced that vector AB would be [k,k,0] for some scalar k because it's parallel to [1,1,0]. Is that the right way to go about it?

First, I tried finding the angle between A and C. I managed to getCosθ = 6k/squareroot(58k²). From there, I deduced thatAB = 6kandAC = sqaureroot(58k²). However, that doesn't really seem to help me much at all.

I also tried using vector subtraction so vector BC = vector AC - vecor AB but I'm not too sure how to go about that. Also, right-angled triangles seem to indicate Pythagoras so maybe that has something to do with it?

Anyway, can somebody please show me how to solve this problem or perhaps provide a starting point?

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Thankyou. Any help is of course, appreciated.