If x, y, z be an arbitrary point lying on a plane P which passes through the points 42, 0, 0,0, 42, 0and 0, 0, 42, then the value of the expression 3+x−11y−192z−122+y−19x−112z−122+z−12x−112y−192−x+y+z14x−11y−19z−12 is equal to:
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a
-45
b
0
c
3
d
39
answer is C.
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Detailed Solution
Equation of the plane is x+y+z=42Suppose that x-11=a, y-19=b, z-12=c⇒a+b+c=0The given expression is 3+x−11y−192z−122+y−19x−112z−122+z−12x−112y−192−x+y+z14x−11y−19z−12 =3+ab2c2+bc2a2+ca2b2−4214abc =3+a3+b3+c3a2b2c2-3abc =3+3abca2b2c2-3abc =3