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find the equation of the line passing through the point P(4,6,2) and the point of the intersection of the line x-1/3=y/2=z+1/7 and the plane x+y-z=8. Plz help me out with this question...

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x-1/3=y/2=z+1/7=k
 
Therefore any point can be represented as(3k+1,2k,7k-1)
 
This point intersects with the plane therefore it satisfies the equation
 
3k+1+2k+1-7k=8
 
-2k=6
 
k=-3;
 
Therefore the point is(-8,-6,-22)
 
Then the equation of a plane passing through (4,6,2) and the points(-8,-6,-22)
 
is r=a+k(b-a)
 
r=4i+6j+2k+k(-12i-12j-24k)
 
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