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Math Help - vectors.lines.planes

  1. #1
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    vectors.lines.planes

    1) Find a vector equation and parametric equations for the line through the origin and parallel to the line x=2t, y=1-t, z=4+3t.

    2) Find parametric and symmetric equations for the line through (2,1,0) and perpindicular to both i+j and j+k

    can someone help me with these? thanks
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by xfyz View Post
    1) Find a vector equation and parametric equations for the line through the origin and parallel to the line x=2t, y=1-t, z=4+3t.
    Hint: you want the line passing through (0,0,0) with direction vector <2,-1,3>

    2) Find parametric and symmetric equations for the line through (2,1,0) and perpindicular to both i+j and j+k
    Hint: you want the line passing through (2,1,0) with direction vector given by <1,1,0> X <0,1,1>, where X means the cross-product
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    Hint: you want the line passing through (0,0,0) with direction vector <2,-1,3>

    Hint: you want the line passing through (2,1,0) with direction vector given by <1,1,0> X <0,1,1>, where X means the cross-product
    1.
    r = ro + tv

    t(2i-j+3k) the vector eq
    x = 2t, y = -t, z = 3t the parametric

    2.
    r = ro+tv after cross product

    v = <1,-1,1>

    r = (2i+j) + t(i-j+k)

    r = i(2+t)+j(1-t)+k(t) the vector eq

    x = 2+t , y = 1-t , z = 1 the parametric

    is this right?
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