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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

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  • $\begingroup$ See here: math.stackexchange.com/questions/2071456/… $\endgroup$ – user371838 Dec 25 '16 at 16:17
  • $\begingroup$ @Rohan in that you have not mentioned about saclar product $\endgroup$ – Koolman Dec 25 '16 at 16:19
  • $\begingroup$ In general we check for coplanarity like that. $\endgroup$ – user371838 Dec 25 '16 at 16:20
  • $\begingroup$ @Rohan can you post an answer in detail explanation. $\endgroup$ – Koolman Dec 25 '16 at 16:25
  • $\begingroup$ 3 vectors or 2 vectors? $\endgroup$ – Fawad Dec 25 '16 at 16:36
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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.

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    $\begingroup$ Could you explain it in more detail $\endgroup$ – Koolman Dec 25 '16 at 16:24
  • $\begingroup$ math.stackexchange.com/questions/2071456/… $\endgroup$ – Koolman Dec 25 '16 at 17:11
  • $\begingroup$ @koolman What i said is correct but downv. $\endgroup$ – hamam_Abdallah Dec 25 '16 at 17:14
  • $\begingroup$ I want to know about scalar product $\endgroup$ – Koolman Dec 25 '16 at 17:19
  • $\begingroup$ @koolman The scalar product tells us about orthogonality of two vectors. $\endgroup$ – hamam_Abdallah Dec 25 '16 at 17:20

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