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A point (2, alpha, beta) lies on a plane that passes through (3, 4, 2) and (7, 0, 6) and is perpendicular to the plane 2x - 5y = 15. Find the value of 2*alpha - 3*beta.
- 2*alpha - 3*beta = 17
- 2*alpha - 3*beta = 7
- The plane passes through (0, 4, -3)
- The plane passes through (0, 0, 0)
Correct answer: 2*alpha - 3*beta = 7
Solution
The direction along the two points and the normal of the perpendicular plane together define the normal to our plane. Using these, the plane equation gives 2*alpha - 3*beta = 7.
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