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Math Help - Show span is a plane through origin

  1. #1
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    Show span is a plane through origin

    Let v1=[x1,y1,z1] and v2=[x2,y2,z2] assume that v1 and v2 are linearly independent, show that span{v1,v2} is a plane passing through the origin. What is the equation of that plane?

    I know to show its a plane we need to show there are 2 degrees of freedom but from there on im pretty lost any help would be grealy appreciated.
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  2. #2
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    Quote Originally Posted by ChrisBickle View Post
    Let v1=[x1,y1,z1] and v2=[x2,y2,z2] assume that v1 and v2 are linearly independent, show that span{v1,v2} is a plane passing through the origin. What is the equation of that plane?

    I know to show its a plane we need to show there are 2 degrees of freedom but from there on im pretty lost any help would be grealy appreciated.
    We can use some Calculus common knowledge to show that v_1 and v_2 are a plane.

    1 vector in 3 space forms a line
    2 vectors in 3 space at most forms a plane and forms a line if they aren't lin. ind.
    Since we are given that v_1 and v_2 are lin. ind., we know they form a plane.

    Example:
    Suppose <1,2,3> is a normal vector to our plane then our equation would be:

    1(x-x_1)+2(y-y_2)+3(z-z_2)=0

    Where (x_3,y_3,z_3) is a point in the plane.

    You are giving a point is the origin (0,0,0). All you need is a normal vector now.
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