The equation of the plane passing through the point (1, 1, 1) and parallel to the plane 2x + 3y − 4z = 5 is:
The equation of the plane passing through the point (1, 1, 1) and parallel to the plane 2x + 3y − 4z = 5 is:
- A. 2x + 3y − 4z = 1
- B. 2x + 3y − 4z = 0
- C. 2x + 3y − 4z = 5
- D. 2x + 3y − 4z = −1
Answer: A) 2x + 3y − 4z = 1
Explanation: Parallel plane has the same normal: 2x + 3y − 4z = k. Substitute (1, 1, 1): 2(1) + 3(1) − 4(1) = k → 5 − 4 = 1. The equation is 2x + 3y − 4z = 1.
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