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Math Help - Vector equations of lines

  1. #1
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    Vector equations of lines

    Can someone please help me with these problems?
    (1) Let A, B, C be the vertices of a triangle. Let a, b, c be their position vectors respectively. Find the equations of the lines through each vertex, perpendicular to the opposite side.
    (2) Find the equations of the perpendicular bisectors of each side of the triangle.
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Vector equations of lines

    Hint - if you know the slope of the line that connects points A and B then the slope of any line that is perpendicular to AB is the negative inverse of the slope of AB. Now use y = mx+b, given the x,y coordinates of point C, to determine the equation of the line that goes through C and is perpendicular to AB.
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    Re: Vector equations of lines

    Thank you for your help but in this question I'm not referring to a 2-coordinate systems with only x and y axes. I'm referring to a coordinate system with x , y and z axes. I need a vector equation in the form : r = a + t(v)
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  4. #4
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    Re: Vector equations of lines

    Quote Originally Posted by Kristen111111111111111111 View Post
    I'm referring to a coordinate system with x , y and z axes. I need a vector equation in the form : r = a + t(v)
    Suppose that U = \overrightarrow {AB} \;,\;V = \overrightarrow {BC} \,\& \,W = \overrightarrow {AC}

    Then the line through A which is perpendicular to \overleftrightarrow {BC} is \vec{a}+t(V\times(U\times W)).

    You finish the other two. Change the notation to suit yourself.
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  5. #5
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    Re: Vector equations of lines

    Thank you so much I got it
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