Three vectors a , b and c are such that a b = c , b c = a , c a = b . Answer the…

Three vectors \(\hat{a}, \hat{b} \text { and } \hat{c}\) are such that
\(\hat{a} \times \hat{b}=\hat{c}, \hat{b} \times \hat{c}=\hat{a}, \hat{c} \times \hat{a}=\hat{b} .\)
Answer the following questions :
Let \(\vec{x}=\hat{a}+\hat{b}, \vec{y}=2 \hat{a}-\hat{b},\) then the point of intersection of straight lines \(\vec{r} \times \vec{x}=\vec{y} \times \vec{x}, \vec{r} \times \vec{y}=\vec{x} \times \vec{y}\)is