Let p = 0 be the equation of a plane passing through the line of intersection of the planes 2x - y = 0 and 3z - y= 0 and perpendicular to the plane 4x + 5y - 3z = 8. Then the points which lie on the plane P:0 is/are
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a
(0,9,17)
b
(1/7,2,1/9)
c
(1, 3, -4)
d
(½,1,⅓)
answer is A.
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Detailed Solution
The equation of the plane passing through the intersection of the planes 2x - y = 0and 3z- y= 0 is 2x−y+λ(3z−y)=0-----ior 2x−y(λ+1)+3λz=0Plane (i) is perpendicular to 4x + 5y - 3z=8. Therefore, 4×2−5(λ+1)−9λ=0or 8−5λ−5−9λ=0or 3−14λ=0or λ=3/142x−y+314(3z−y)=028x−17y+9z=0