1003188803 | math4u.vsb.cz

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1003188803

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A plane

ρ

is defined by the point

A = [3; 1; 1]

and a straight line

p

defined by the following parametric equations:

\begin{aligned} p : x & = 4 + 4 t, \\ y & = - 1 - 2 t, \\ z & = 1 + t; t \in R \end{aligned}

Find the parametric equations of the plane

ρ

.

\begin{aligned} ρ : x & = 4 + 4 t + s, \\ y & = - 1 - 2 t - 2 s, \\ z & = 1 + t; t, s \in R \end{aligned}

\begin{aligned} ρ : x & = 4 + 4 t + 3 s, \\ y & = - 1 - 2 t + s, \\ z & = 1 + t + s; t, s \in R \end{aligned}

\begin{aligned} ρ : x & = 3 + 4 t + 4 s, \\ y & = 1 - 2 t - s, \\ z & = 1 + t + s; t, s \in R \end{aligned}

\begin{aligned} ρ : x & = 3 + 4 t - 4 s, \\ y & = 1 - 2 t + 2 s, \\ z & = 1 + t - s; t, s \in R \end{aligned}