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Equation of plane question?

Vector Equation of a plane Textbook question?

  • I need help with this vectors question from "Calculus and Vectors 12" BEEN STUCK ON IT FOR AN HOUR :0 Okay, so it goes like this: Write the equation of the plane that contains points A(3,0,4) B(2,-3,1) C(-5,8,-4) and D(1,4,3), if it exists. Textbook Answer: [x,y,z] = [3,0,4] + s[1,3,3] + t[1,-1,1] Any ideas? If you have the textbook its question 16 on page 452. Thanks in advance!

  • Answer:

    Actually, it's trivial to get the parametrized equation of a plane from three non-collinear points: [x,y,z] = A + s(A-B) + t(A-C) In your example, A-C is not in lowest terms; a common factor of 8 has been extracted and hidden in "t". All you need to do then is to see whether D satisfies the equation for some values of s and t. Getting the equation in standard form is a little more involved. http://en.wikipedia.org/wiki/Plane_%28geometry%29

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Actually, it's trivial to get the parametrized equation of a plane from three non-collinear points: [x,y,z] = A + s(A-B) + t(A-C) In your example, A-C is not in lowest terms; a common factor of 8 has been extracted and hidden in "t". All you need to do then is to see whether D satisfies the equation for some values of s and t. Getting the equation in standard form is a little more involved. http://en.wikipedia.org/wiki/Plane_%28geometry%29

norcekri

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