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Math Help - Equation of a plane

  1. #1
    Member nautica17's Avatar
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    Equation of a plane

    This is a question from my calculus 3 class.

    "Find an equation of the plane through the point (-1,4,2) that contains the line of intersection of the planes (4x - y + z - 2) = 0 and (2x + y - 2z - 3) = 0."

    I'm having problems trying to figure this out. I get an answer but it's different than what the book says it is.

    My work:
    v1 = <4,-1,1>
    v2 = <2,1,-2>

    v1 x v2 = i + 10j + 6k

    Point-normal form equation of plane:
    (x+1) + 10(y-4) + 6(z-2) = 0
    x + 1 + 10y - 40 + 6z - 12 = 0
    x + 10y + 6z = 51 <---- my answer?

    The book says the answer is 4x - 13y + 21z = -14, and more than likely it is correct and not me in this case.
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  2. #2
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    Step 1: Find the line of intersection of the planes.

    Step 2: Find two points on this line.

    Step 3: The two points on your line that you found in step 2, along with the point (-1, 4, 2), can be used to find the equation of the plane.
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  3. #3
    Member nautica17's Avatar
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    Cool, I'm going to do that.
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