Find the angle between the plane passing through points (1, 1, 1), (1, − 1, 1), ( − 7, − 3, − 5) & x − z plane.
Text Solution
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(π /2)
Sol. Equation of plane passing through (1, 1, 1) is a(x – 1) + b(y – 1) + c(z – 1) = 0 ... (1)
it passes through (1, – 1, 1) and (– 7, – 3, – 5)
∴ a.0 – 2.b + 0.c = 0 ⇒ b = 0 and – 8a – 4b – 6c = 0
4a + 2b + 3c = 0 b = 0
∴ 4a + 3c = 0 ⇒ c = 
∴ dr’s of normal to the plane are 1, 0 – 
and dr’s of the normal to the x-z plane are 0, 1, 0
∴ cos θ = 
∴ θ = 
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