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 .

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

See here: http://math.stackexchange.com/questions/2071456/coplanar-lines-in-3d-plane/2071461#2071461 — , Dec 25 '16 at 16:17

hamam_Abdallah · Answer 1 · 2016-12-25T17:23:47.803

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.

edited Dec 25 '16 at 17:23

answered Dec 25 '16 at 16:19

hamam_Abdallah

1

Could you explain it in more detail – Koolman Dec 25 '16 at 16:24
http://math.stackexchange.com/questions/2071456/coplanar-lines-in-3d-plane/2071461#2071461 – Koolman Dec 25 '16 at 17:11
@koolman What i said is correct but downv. – hamam_Abdallah Dec 25 '16 at 17:14
I want to know about scalar product – Koolman Dec 25 '16 at 17:19
@koolman The scalar product tells us about orthogonality of two vectors. – hamam_Abdallah Dec 25 '16 at 17:20

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