Barnett Griffin
08/07/2024 · Senior High School

6. Find the parametric vector equation of that passes through \( (1,4) \) and i. Parallel to the line \( y=3 x-1 \) ii. Perpendicular to the line \( x-2 y=5 \) 7. Find equation of of the plane passing through the given points

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For Problem 6: i. The parametric vector equation of the line parallel to \( y = 3x - 1 \) and passing through \( (1, 4) \) is \( \mathbf{r}(t) = \begin{pmatrix} 1 + t \\ 4 + 3t \end{pmatrix} \). ii. The parametric vector equation of the line perpendicular to \( x - 2y = 5 \) and passing through \( (1, 4) \) is \( \mathbf{r}(t) = \begin{pmatrix} 1 - t \\ 4 + 2t \end{pmatrix} \). For Problem 7, the equation of the plane can be found using the coordinates of the points provided.

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