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The equation of the plane passing through the points (2, 1, 0), (3, – 2, – 2) and (3, 1, 7) is:​
  • a)
    7x + 3y – z = 17
  • b)
    7x + 3y – 2z = 21
  • c)
    7x + 3y – z = 21
  • d)
    -7x – 3y + z = 17
Correct answer is option 'A'. Can you explain this answer?
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Finding the equation of a plane passing through three points requires finding the normal vector of the plane and using one of the points to obtain the equation. Here's how to do it:

Finding the Normal Vector:
- Choose two of the points, say A(2, 1, 0) and B(3, 2, 2)
- Find the vector AB: AB = (3-2)i + (2-1)j + (2-0)k = i + j + 2k
- Choose another point, say C(3, 1, 7)
- Find the vector AC: AC = (3-2)i + (1-1)j + (7-0)k = i + 7k
- Find the cross product of AB and AC: N = AB x AC = (1-7) i - (2-0)j + (2-1)k = -6i - 2j + k
- The normal vector of the plane is N = (-6, -2, 1)

Writing the Equation of the Plane:
- Using the point A(2, 1, 0), we have:
- -6(x-2) - 2(y-1) + 1(z-0) = 0
- Simplifying, we get:
- -6x + 12 - 2y + 2 + z = 0
- Rearranging, we get:
- 7x - 3y + z = 17

Therefore, the equation of the plane passing through the points (2, 1, 0), (3, 2, 2) and (3, 1, 7) is 7x - 3y + z = 17, which is option A.
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The equation of the plane passing through the points (2, 1, 0), (3, – 2, – 2) and (3, 1, 7) is:​a)7x + 3y – z = 17b)7x + 3y – 2z = 21c)7x + 3y – z = 21d)-7x – 3y + z = 17Correct answer is option 'A'. Can you explain this answer?
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The equation of the plane passing through the points (2, 1, 0), (3, – 2, – 2) and (3, 1, 7) is:​a)7x + 3y – z = 17b)7x + 3y – 2z = 21c)7x + 3y – z = 21d)-7x – 3y + z = 17Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The equation of the plane passing through the points (2, 1, 0), (3, – 2, – 2) and (3, 1, 7) is:​a)7x + 3y – z = 17b)7x + 3y – 2z = 21c)7x + 3y – z = 21d)-7x – 3y + z = 17Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation of the plane passing through the points (2, 1, 0), (3, – 2, – 2) and (3, 1, 7) is:​a)7x + 3y – z = 17b)7x + 3y – 2z = 21c)7x + 3y – z = 21d)-7x – 3y + z = 17Correct answer is option 'A'. Can you explain this answer?.
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