MHB Find k & m for Perpendicular Line to U, W & V Plane

[shawen]

find the values of k and m so that the line x+1/k = y-2/m = z+3/1 is perpendicilar to the plane through the points U(1,3,8) , W(0,1,1) , and v(4,2,0).PLEASE HELP ME
THANKS ALOT :)

 

[Euge]

find the values of k and m so that the line x+1/k = y-2/m = z+3/1 is perpendicilar to the plane through the points U(1,3,8) , W(0,1,1) , and v(4,2,0).PLEASE HELP ME
THANKS ALOT :)

The equation of the line shows that the line is parallel to the vector $<k, m,1>$. A normal to the plane is

$\vec{UW} \times \vec{WV} =\, <-1,-2,-7> \times <4,1,-1> =\, <9,-29,7>$.

For the line to be perpendicular to the plane, the normal $<9,-29,7>$ must be parallel to $<k, m, 1>$. So what does that tell you about $k$ and $m$?