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    vectors

    What is the z component of a vector parallel to the x-y plane ? explain
    find all unit vectors parallel to the x-y plane and perpendicular to the vector [1,-2, 2 ]
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    Quote Originally Posted by fastman390 View Post
    What is the z component of a vector parallel to the x-y plane ? explain
    find all unit vectors parallel to the x-y plane and perpendicular to the vector [1,-2, 2 ]
    In \mathbb{R}^3 any vector in the xy plane has no vertical component so its z component is zero.

    for part two

    is the vector is parallel to the xy plane it is perpendicular to the z axis

    again let <x,y,z> be any vector so we know that

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

     <x,y,0> \cdot <1,-2,2>=0 \iff x-2y=0 \iff x=2y

    so we get

    <x,2x,0> =x<1,2,0>

    To make this a unit vector divide each component of the vector by the vectors magnitude!
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