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+2 votes
10.4k views
in Mathematics by (31.4k points)

If the equation of the plane passing through the line of intersection of the planes 2x – 7y + 4z – 3 = 0, 3x – 5y + 4z + 11 = 0 and the point (–2, 1, 3) is ax + by + cz – 7 = 0, then the value of 2a + b + c – 7 is _____.

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1 Answer

+3 votes
by (30.9k points)

Answer is (4)

Required plane is

which is satisfied by (–2, 1, 3).

Hence, λ = \(\frac{1}{6}\)

Thus, plane is 15x - 47y + 28z - 7 = 0

So, 2a + b + c - 7 = 4

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