7_Lines_Planes - Lines and Planes Lines Let Let P0(a, b, c)...

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Lines and PlanesLinesLetlbe a line parallel to vectorv.v=v1i+v2j+v3kLetP0(a,b,c)be a point on the line andP(x,y,z)be anyother point on the line.P0Pis a vector parallel to the line.P0PvsoThe parametric equations of a line are:x=a+v1ty=b+v2tz=c+v3t
To find the equation of a line you need a point on the line and avector parallel to the line.ex. Find the equation of the line through P(1, 5, 3) parallel tovectorv=2, 0, 1=2i+kex. Find the equation of the line through points P(1, 2, 3) andQ(3, 6, 9).ex. Find a vector parallel to the line.
x=9-ty=3z=6tex.Determine which of the following line equations represent thesame line asx=9-ty=3z=6tx1=7+2tx2=11-3tx3=9+ty1=3y2=3y3=3z1=12-12tz2=10+18tz3=6tPlanes
LetP0(a,b,c)be a point in the plane.If P(x, y, z) is any otherpoint in the plane, thenP0Pis a vector that lies in the plane.Letn=n1i+n2j+n3kbe a vector perpendicular (normal) to theplane.Then
The equation of a plane isn1x+n2y+n3z=npwherenis the normal vector andpis the vector formed by the point.To find the equation of a plane you need a point on the plane and avector normal (perpendicular) to the plane.
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