Find normal vector to plane given two line equation
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Determine an equation of the plane containing the lines x−12=y+1−1=z−56x−12=y+1−1=z−56; r=<1,−1,5>+t<1,1,−3>r=<1,−1,5>+t<1,1,−3>.
I calculated the cross product between the directional vector of both lines to find the normal vector nn, but when I looked for an intersection point r0r0 to apply the formula: <r−r0>∙ n<r−r0>∙ n, I did not find any.
Can I use the point <1,−1,5><1,−1,5> given in the line rr? Or is it not possible to find an equation of the plane containing two lines that do not intersect?
I calculated the cross product between the directional vector of both lines to find the normal vector nn, but when I looked for an intersection point r0r0 to apply the formula: <r−r0>∙ n<r−r0>∙ n, I did not find any.
Can I use the point <1,−1,5><1,−1,5> given in the line rr? Or is it not possible to find an equation of the plane containing two lines that do not intersect?
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