# Intersect

• Apr 12th 2008, 09:41 AM
fastman390
Intersect
find the value of k such that the line x-1 = y-2 = z-k and the plane
3 1 5
2x-y-z+10 = 0 intersect only at one pin .
• Apr 12th 2008, 10:01 AM
TheEmptySet
Quote:

Originally Posted by fastman390
find the value of k such that the line x-1 = y-2 = z-k and the plane
3 1 5
2x-y-z+10 = 0 intersect only at one pin .

I don't have time for a full solution,but try this

converted the symmetric equations into parametric form and sub into the equation of the plane. see what happens

Good luck.
• Apr 12th 2008, 10:26 AM
TheEmptySet
Quote:

Originally Posted by fastman390
find the value of k such that the line x-1 = y-2 = z-k and the plane
3 1 5
2x-y-z+10 = 0 intersect only at one pin .

we have that
$\frac{x-1}{3}=\frac{y-2}{1}=\frac{z-k}{5}$

setting each equal to t we can get the parametric form.

$\frac{x-1}{3}=t \iff x=3t+1$

doing the same for the others gives

$y=t+2 \mbox{ and } z=5t+k$

plugging these into the equation of the plane gives
$2(3t+1)-(t+2)-(5t+k)+10=0 \iff -k+10 =0 \iff k=10$