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...or any other vector in the without a y component

Determine the vector v, orthogonal to the axis Oy.

where v*v1=8 and v*v2=-3

you did not really clarify you just repeated yourself
are these dot products?

Yes these are dot products

then the y component can be left away, will result in a system of equations.

Here it´s a shot from the book where i taken the question.

And, what´s more?

yep

x=2, z=-1, is what I got if you want to compare.

Yes, that´s for sure. x=2 and z=-1. Thanks guys.

So the answer to the question is w=(2,0,-1)

Thanks for the help. But, i don´t know how to use the Latex yet. Thanks a lot for the help.