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anonymous
 4 years ago
find a vector equation and parametric equations through the point (1,0,6) and perpendicular to the plane x + 3y + z =5
anonymous
 4 years ago
find a vector equation and parametric equations through the point (1,0,6) and perpendicular to the plane x + 3y + z =5

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amistre64
 4 years ago
Best ResponseYou've already chosen the best response.2is the point on a line? thru the plane?

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.2if so, the normal of the plance is the perp to it; strip off your coeefs for the line vector: <1,3,1> would be the vector that is perpenducular to the plane

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.2since 1,0,6 is not on the plane im going to assume its on the line perp to it (the perp line is called a normal)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0okay I'm with you so far

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.2x = Px + 1t y = Py + 3t z = Pz + 1t given the point (1,0,6) this makes x = 1 + 1t y = 0 + 3t z = 6+ 1t

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0okay but why are the points (1,3,1) perpendicular to the plane?

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.2its a result of how the equation of a plane is defined

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.2the perp to the plane is a vector that dot producted to every line in the plane

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.2so given a point (Px,Py,Pz) in space: we can construct any vector from it by taking any random point (x,y,z) and subtracting the 2 of them: (xPx, yPy, zPz) is every vector that comes out from our point into space

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.2to elimante all the vectors that are not in a plane; we need to establish a perp vector to it so that when we dot it to these vectors we get 0, so all vectors of the form: (xPx,yPy,zPz) dot (Nx,Ny,Nz) = 0 Nx(xPx) +Ny(yPy) +Nz(zPz) = 0 is the equation of the plane

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0you're way better at explaining things than my book...

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.2thats becasue im crazy lol

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0lol, does normal mean perpendicular?

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.1Actually, yes in this context. The word normal is used for other things in maths elsewhere.
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