1003233605 | math4u.vsb.cz

SubArea:

Level:

Project ID:

1003233605

Source Problem:

Accepted:

1

Clonable:

1

Easy:

0

We are given skew lines

p

and

q

.

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

Find parametric equations of a straight line

r

, that is intersecting both lines

p

and

q

and lying in the plane

x + 2 y - z + 2 = 0

.

\begin{aligned} r : x & = - 1 + 2 m, \\ y & = 3 - 3 m, \\ z & = 7 - 4 m; m \in R \end{aligned}

\begin{aligned} r : x & = - 1 + m, \\ y & = 3 + 3 m, \\ z & = 7 - m; m \in R \end{aligned}

\begin{aligned} r : x & = - 1 + 3 m, \\ y & = 3 + 2 m, \\ z & = 7 + 5 m; m \in R \end{aligned}

\begin{aligned} r : x & = - 1 + m, \\ y & = 3 - m, \\ z & = 7 + m; m \in R \end{aligned}