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The coordinates of the foot of the perpe...

The coordinates of the foot of the perpendicular from the point `(1,-2,1)` on the plane containing the lines, `(x+1)/6=(y-1)/7=(z-3)/8` and `(x-1)/3=(y-2)/5=(z-3)/7`, is (a,b,c) then a+b+c=

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The correct Answer is:
0
`vecn = vec(n_1) xx vec(n_2) = |{:(hati , hatj , hatk),(6,7,8),(3,5,7):}| = (9,-18,9) = (1,-2,1)`
`therefore ` Equation of plane is
`1(x+1) - 2(y-1) + (z-3)=0`
`implies x-2y + z =0`
Foot of perpendicular is
`(x-1)/(1)= (y+2)/(-2) = (z-1)/(1) = ([1+4+1])/(6)`
`x= 0, y=0 , z=0`
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