The mirror image of P (2 ,4 ,-1 ) in the plane x-y +2z-2=0 is (a ,b ,c ), then the value of a+b+c is

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Correct answer: D. (d) : Let M (a ,b ,c ) be the image of P (2 ,4 ,-1 ) in the plane x-y+2z-2=0 ∴ Equation of line passing through P (2 ,4 ,-1 ) and having direction ratio (1 ,-1 ,2 ) is x-21= y-4-1= z+12=k ( let ) Any point on this line is of the form (k+2 ,-k+4 ,2k-1 ). Substituting this point in equation of plane, we get k+2- (-k+4 )+2 (2k-1 )-2=0 ⇒k+2+k-4+4k-2-2=0 ⇒6k-6=0 ⇒k=1 ∴ Q (3 ,3 ,1 ) lies on the plane. As M (a ,b ,c ) is the image of P (2 ,4 ,-1 ) in the plane x-y+2z-2=0. ∴ Q is midpoint of PM. ⇒3= a+22 ,3= b+42 and 1= -1+c2 ⇒a=4 ,b=2 ,c=3 ∴a+b+c=4+2+3=9

$The mirror image of P (2, 4, - 1) in the plane x - y + 2 z - 2 = 0 is (a, b, c), then the value of a + b + c is$

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