Let a line with direction ratios a , - 4 a , - 7 be perpendicular to the lines with direction ratios 3 , - 1 , 2 b and b , a , - 2 . If the point of intersection of the line x + 1 a 2 + b 2 = y - 2 a 2 - b 2 = z 1 and the plane x - y + z = 0 is α , β , γ , then α + β + γ is equal to ________.

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Given a line with direction ratios a , - 4   a , - 7 be perpendicular to the lines with direction ratios 3 , - 1 , 2 b and b ,   a , - 2 . If the point of intersection of the line x + 1 a 2 + b 2 = y - 2 a 2 - b 2 = z 1 and the plane x - y + z = 0 is α , β , γ , then α + β + γ is equal to ________. Now given a , - 4 a , - 7 ⊥ to 3 , - 1 , 2 b So, 3 a + 4 a - 14 b = 0 ⇒ a = 2 b           ⋯ i Also a , - 4 a , - 7 ⊥ to b , a , - 2