Equations of lines in 3 Dimension

  • If cos α, cos β and cos γ are the direction cosines of a line then cos2 α + cos2 β + cos2 γ = 1

  • If cos α, cos β and cos γ are the direction cosines of a line passing through the point (a,b,c) then
    (x - a)/cos α = (y - b)/cos β = (z - c)/cos γ is the equation of the line.

  • If (x1, y1, z1) and (x2, y2, z2) are two points through which a line pass then
    (x - x1)/(x2 - x1) = (y - y1)/(y2 - y1) = (z - z1)/(z2 - z1) is the equation of the line.



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