alleryThe angle between the planes 2x - y + 2z = 5 and x + 2y - 2z = 4 satisfies
Acos θ = -4/9
Bcos θ = 4/9
Ccos θ = -2/3
Dcos θ = 0
Answer & Solution
Correct answer: A. cos θ = -4/9
1. Normal to first plane: (2, -1, 2); magnitude √(4+1+4) = 3.
2. Normal to second plane: (1, 2, -2); magnitude √(1+4+4) = 3.
3. Dot product of normals: 2(1) + (-1)(2) + 2(-2) = -4.
4. cos θ = -4 / (3·3) = -4/9.
_Source: syllabus Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.8_
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