The Lines $l _ { 1 } :$ $\mathbf { r } _ { 1 } = \langle 2,3,1 \rangle+ t \langle - 1,1,1 \rangle$

Essay

The lines $l _ { 1 } :$ $\mathbf { r } _ { 1 } = \langle 2,3,1 \rangle+ t \langle - 1,1,1 \rangle$ and l₂: $\mathbf { r } _ { 2 } = \langle 3,1,2 \rangle + s \langle - 1,2 , - 1\rangle$ both contain the point P (2, 3, 1). Find the value of s which gives the point of intersection P, and then compute the angle $\theta$ between the two lines.