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Math Help - Calculus 4: equation of a plane

  1. #1
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    Calculus 4: equation of a plane

    Hello everyone,

    Could someone please help me on this problem?

    A plane has equation z=5x-2y+7

    a. Find the value of W making the vector Wi+j+.5k normal to the plane

    b. Find a value of a so that the point (a+1, a, a-1) lies on the plane

    My attempt:

    z=5x-2y+6
    Wi+1j+.5k

    a. 1j--> -2y
    -.5--> 7

    5(x-01)-2(y-0)+5(z-0)+7=0

    b.

    5(x-a+1)-2(y-a)+0(a-1)+7=0

    I now just need to solve for a, righ?

    Is this anywhere close?

    Thank you very much
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Chocolatelover2 View Post
    Hello everyone,

    Could someone please help me on this problem?

    A plane has equation z=5x-2y+7

    a. Find the value of W making the vector Wi+j+.5k normal to the plane

    b. Find a value of a so that the point (a+1, a, a-1) lies on the plane

    My attempt:

    z=5x-2y+6
    Wi+1j+.5k

    a. 1j--> -2y
    -.5--> 7

    5(x-01)-2(y-0)+5(z-0)+7=0
    why are you working so hard?

    the plane is -5x + 2y + z = 7

    thus the normal vector is <-5,2,1> we want a vector that is parallel to this with coordinates <w, 1 , 1/2>

    note that <w, 1, 1/2> = k<-5, 2, 1> for some constant k

    b.

    5(x-a+1)-2(y-a)+0(a-1)+7=0

    I now just need to solve for a, righ?

    Is this anywhere close?

    Thank you very much
    plug in x = a + 1, y = a, z = a - 1, then we have

    -5(a + 1) + 2a + (a - 1) = 7

    just solve for a
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  3. #3
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    Thank you very much

    That's a lot easier!

    For a, I just need to find the equation that is parallel to 5x-2y-z=-7 through (-5,2,1) and (w, 1, 1/2), right? Would I use a matrix?

    Thank you
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Chocolatelover2 View Post
    Thank you very much

    That's a lot easier!

    For a, I just need to find the equation that is parallel to 5x-2y-z=-7 through (-5,2,1) and (w, 1, 1/2), right? Would I use a matrix?

    Thank you
    all you are doing is finding a value for w that makes <w, 1, 1/2> parallel to <-5, 2, 1>

    all you have to do is find the constant k that i mentioned. it is not hard, you do not need matrices. just set up a simple equation to relate them
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