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(Step-by-Step) (a) Determine a vector equation r(t)=\mathrmr_0+t • v for the line that passes through the point P(1,2,3) and is perpendicular to the

Question: (a) Determine a vector equation \(\mathrm{r}(t)=\mathrm{r}_{0}+t \cdot \mathbf{v}\) for the line that passes through the point \(P(1,2,3)\) and is perpendicular to the plane \(4 x+5 y+6 z=7\)

(b) Consider the planes

\[\begin{aligned} x-\frac{1}{5} y+\frac{2}{5} z &=42 \text { and } \\ \langle 3,-4,5\rangle \cdot(\langle x, y, z\rangle-\langle 0,2,4\rangle) &=0 \end{aligned}\]

in \(\mathbb{R}^{3}\). If these planes are parallel, determine their distance. Otherwise determine their angle of intersection.

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