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.

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The Answer of 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.

The Lines l1:l _ { 1 } :l1​: r1=⟨2,3,1⟩+t⟨−1,1,1⟩\mathbf { r } _ { 1 } = \langle 2,3,1 \rangle+ t \langle - 1,1,1 \rangler1​=⟨2,3,1⟩+t⟨−1,1,1⟩

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