Lines and Planes in 3-DLinear Equations: In 2-D: Ax+By=CWhat is the graph? DWhat is the graph? Review Parametric EquationsGeneral 2-D: Example: x=f(t)y=g(t)x=t2y=4t2What about 3-D?
Lines in 3-DGiven: P1(x1,y1,z1)is a specific point on the line v=a,b,cis a vector parallel to the line Find: Parametric Equations to describe all of the points P(x,y,z)on the line
Parametric Equations for the line that passes through the point P(x1,y1,z1)and is parallel to the vector v =a,b,cx=x1+aty=y1+btz=z1+ct___________________________________________________ Find parametric equations for the line that passes through P1(4,−1,3)and is parallel to v=2,1,−4Does the point Q(6,0,−1)lie on the line? Does the point R(1,2,−3)lie on the line? Is the line parallel to the vector w=−4,−2,8Is the line parallel to the vector w=6,3,−4: . ? ?