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31/01/2022 1:34 pm
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Let the equation of the plane, that passes through the point (1, 4, -3) and contains the line of intersection of the planes 3x – 2y + 4z – 7 = 0 and x + 5y – 2z + 9 = 0, be αx + βy + γz + 3 = 0, then α + β + γ is equal to
(1) -23
(2) -15
(3) 23
(4) 15
1 Answer
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31/01/2022 1:39 pm
Correct answer: (1) -23
Explanation:
Equation of plane is
3x – 2y + 4z – 7 + λ(x + 5y – 2z + 9) = 0
(3 + λ)x + (5λ – 2)y + (4 – 2λ)z + 9λ – 7 = 0
passing through (1, 4, –3)
⇒ 3 + λ + 20λ – 8 – 12 + 6λ + 9λ – 7 = 0
⇒ λ = \(\frac{2}{3}\)
⇒ equation of plane is
-11x - 4y - 8z + 3 = 0
⇒ α + β + γ = -23