Condition for two line to be coplanar

Question

I want to know what is the condition for two lines to be coplanar . I searched it on internet.

I found that for coplanar the scalar product should be zero .

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But I could not understand why it should be zero . And what are the three vectors whose scalar product is zero

Answer 1

Hint

The lines are parallel or intersect if not they are not coplanar. use parametric equations of a line :

$$x=a+ut$$ $$y=b+vt$$ $$z=c+wt$$ where $(a,b,c)$ is a point of the line, $(u,v,w)$ the vector director and $t$ a parameter.