Explanation
Three vectors a, b and c are said to form a right handed system if a right threaded screw when rotated from a to b the screw moves in direction of c.
Even you can say that axb=c
\vec{c}= \begin{vmatrix}\hat{i}&\hat{j}&\hat{k} \\x&y&z\\0&1&0\end{vmatrix}
\vec{c}=\hat{i}(-z)-\hat{j}(0)+\hat{k}(x)
\vec{c}=-z\hat{i}+x\hat{k}
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