A question from 3d geometry: Find the equation of the plane passing through the points $(1,2,3)$ and $(0,-1,3)$ and parallel to the line $R=i-2j+t(2i+3j-3k)$?
3d geometry please help
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linear-algebra
geometry
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0no i found this little difficult so i posted #zipirovich – 2017-02-21
1 Answers
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To find an equation of a plane in $\mathbb{R}^3$, you need two things: a point in the plane and a vector normal to the plane. In this examples, you have the two given points to choose from, so the main goal here is to find a normal vector. Note that the given information allows you to find two vectors that lie in the plane: the directional vector of the given line (which you can see from the line's equation) and the vector connecting the two points in the plane. A normal vector would have to be perpendicular to both of them. Do you know which vector operation can take two vectors and create a result that's perpendicular to both of them?
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0thanks@zipirovich i got it – 2017-02-22