2010008908 | math4u.vsb.cz

SubArea:

Level:

Project ID:

2010008908

Source Problem:

Accepted:

0

Clonable:

1

Easy:

0

We are given skew lines

a

and

b

.

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

Find parametric equations of a straight line

p

, that is intersecting both lines

a

and

b

and lying in the plane

2 x + 3 y - z - 8 = 0

.

\begin{aligned} p : x & = - 9 + r, \\ y & = 10 + r, \\ z & = 4 + 5 r; r \in R \end{aligned}

\begin{aligned} p : x & = - 9 - 2 r, \\ y & = 10 - 2 r, \\ z & = 4 + 10 r; r \in R \end{aligned}

\begin{aligned} p : x & = - 9 - 10 r, \\ y & = 10 + 9 r, \\ z & = 4 - r; r \in R \end{aligned}

\begin{aligned} p : x & = - 9 + 2 r, \\ y & = 10 + 2 r, \\ z & = 4 - 2 r; r \in R \end{aligned}