Parametric line and point

NaN-Gram

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I feel confused on what to do next, any help would be appreciated.
 

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I feel confused on what to do next, any help would be appreciated.
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What forms have you learned for the equation of a plane?

If you know a form that involves the normal vector, you might consider using a cross product to obtain the normal.
 
We re given: d=<3,5,2>,  Q:(8,2,6)  P:(3,4,1)\vec{d}=<-3,5,2>,\; Q:(8,-2,6)\;P:(3,4,-1) so the line (t)=Q+td\ell(t)=Q+t\vec{d}.
You are required to show that P(t)P\notin \ell(t) so if N=QP×d\vec{N}=\overrightarrow {QP}\times \vec{d}
So that the plane π:N<x8,y+2,z6>=0\pi:\vec{N}\cdot<x-8,y+2,z-6>=0




 
Ok, but what am I taking a cross product of? Would it be r(t) and a line that contains the point P?
That's for you to decide; the goal of an exercise like this is for you to practice thinking, not to depend on others.

But you take cross products of vectors, not lines; and a key idea is that the cross product of two vectors is perpendicular to both of them. So, what vectors do you know, and is there a vector you need to find that is perpendicular to them? Think!
 
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