Calculus III - Vectors: point of intersection; equation of the plane

I am going through a study guide and the following are stumping me:

1.) Find the point of intersection of each of the following pairs of lines, if it exists. If a pair of lines does not intersect, indicate why not.

x = 5t + 3, y = 2t + 1, z = t - 1

x = 2s + 3, y = -s + 10, z = 2s - 2

The lines do not intersect, but I must show why not. Someone please explain?

2.) Find an equation of the plane through (8,1,3) and having a normal vector <3,5,2>

All help would be appreciated. Thank you!

Re: Calculus III - Vectors: point of intersection; equation of the plane

Quote:

Originally Posted by

**Roleparadise** 1.) Find the point of intersection of each of the following pairs of lines, if it exists. If a pair of lines does not intersect, indicate why not.

x = 5t + 3, y = 2t + 1, z = t - 1

x = 2s + 3, y = -s + 10, z = 2s - 2

Solve this system $\displaystyle 5t+3=2s+3~\&~2t+1=-s+10$.

Then show the solution does not work for the $\displaystyle z$ coordinate.