What is the angle between the planes 2x − y + z = 6 and x + y + 2z = 7?
What is the angle between the planes 2x − y + z = 6 and x + y + 2z = 7?
- A. 30°
- B. 45°
- C. 60°
- D. 90°
Answer: C) 60°
Explanation: Normals are n₁ = (2, −1, 1) and n₂ = (1, 1, 2). cos θ = |(2)(1) + (−1)(1) + (1)(2)| / [√(4+1+1) * √(1+1+4)] = |2 − 1 + 2| / [√6 * √6] = 3 / 6 = 1/2. θ = 60°.
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