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  1. #1
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    perpendicular

    Determine a vector perpendicular to both y-axis and the vector with tail at A( 1,1,0) and head at B( 3,9,2) .
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    Quote Originally Posted by fastman390 View Post
    Determine a vector perpendicular to both y-axis and the vector with tail at A( 1,1,0) and head at B( 3,9,2) .
    <
    so the y axis is <0,1,0> and B-A=<2,8,2>

    let <x,y,z> be an aribitary vecotor then


    since we want them to be perpendicular their dot products must be zero so

    <x,y,z> \cdot <0,1,0> \iff y=0

    now

    <x,0,z> \cdot <2,8,2> =0 \iff 2x+2z=0 \iff x=-z

    Now we get

    <-z,0,z>=z<-1,0,1>

    so <-1,0,1> is perpendicualr to both.

    I hope this helps
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