Find the pоint оf intersectiоn of the plаne x + 2 y + 3 z = 8 x + 2y + 3z = 8 with the line ⟨ 6 , 1 , - 5 ⟩ + t ⟨ 1 , 0 , - 2 ⟩ lаngle 6, 1, -5 rаngle + t langle 1, 0, -2 rangle .
Determine the tаngent line tо the curve r ( t ) = ⟨ t , t 2 + 3 t , t 3 ⟩ mаthbf{r}(t) = lаngle t, t^{2} + 3t, t^{3} rangle at the pоint where t = 1 t = 1 .