eb5794…: “Next to the heavy chord”

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Find the equation of the line which passes through the point of intersection of the lines $\vecl _{1}(t)$ and $\vecl _{2}(t)$ and is orthogonal to both lines where $\vecl _{1}(t)=\vector {0,-2,1}+t\vector {1,2,1}$ and $\vecl _{2}(t)=\vector {2,2,3}+t\vector {1,-1,2}$ . Express your answer as a vector and as parametric equations. $\text {Vector: } \vecl (t)=\vector {\answer {2},\answer {2},\answer {3}}+t\vector {5,\answer {-1},\answer {-3}}$ $\text {Parametric: } x(t)=\answer {2+5t},\ y(t)=\answer {2-t},\ z(t)=\answer {3-3t}$