find the value of k such that the linex-1=y-2=z-kand the plane

3 1 5

2x-y-z+10 = 0 intersect only at one pin .

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- Apr 12th 2008, 09:41 AMfastman390Intersect
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 AMTheEmptySet
- Apr 12th 2008, 10:26 AMTheEmptySet
we have that

$\displaystyle \frac{x-1}{3}=\frac{y-2}{1}=\frac{z-k}{5}$

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

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

doing the same for the others gives

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

plugging these into the equation of the plane gives

$\displaystyle 2(3t+1)-(t+2)-(5t+k)+10=0 \iff -k+10 =0 \iff k=10$