A plane cuts the coordinate axes X ,Y ,Z at A ,B ,C respectively such that the centroid of the △ ABC is (6 ,6 ,3 ). Then the equation of that plane is

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Accepted Answer

Correct answer: D. (d) Equation of the plane which cuts the coordinates axes x ,y, and z at a ,b and c respectively, xa+ yb+ zc=1 Centroid G= ( a+0+03 , 0+b+03 , 0+0+c3 ) (6 ,6 ,3 )= ( a3 , b3 , c3 ) Therefore, a=18 ,b=18 ,c=9 The equation of the plane becomes x18+ y18+ z9=1 ⇒ x+y+2z18=1x+y+2z=18 ∴ x+y+2z-18=0

$A plane cuts the coordinate axes X, Y, Z at A, B, C respectively such that the centroid of the △ ABC is (6, 6, 3) . Then the equation of that plane is$

Solution

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