Lines and Planes in 3-DLinear Equations:In 2-D:Ax+By=What is the graph?CD
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What is the graph?Review Parametric EquationsGeneral 2-D:Example:x=f(t)y=g(t)x=t2y=4t2What about 3-D?General 3-D:Example:x=f(t)y=g(t)z=h(t)x=t2y=4t2z=t2+1
Lines in 3-DGiven:P1(x1,y1,z1)is a specific point on the linev=a,b,cis a vector parallel to the lineFind:Parametric Equations to describe all of the pointsP(x,y,z)on the line
Parametric Equations for the line that passes through the pointP(x1,y1,z1)and is parallel to the vectorv=a,b,c:x=x1+aty=y1+btz=z1+ct___________________________________________________Find parametric equations for the line that passes throughP1(4,−1,3)and is parallel tov=2,1,−4.Does the pointQ(6,0,−1)lie on the line?Does the pointR(1,2,−3)lie on the line?Is the line parallel to the vectorw=−4,−2,8?Is the line parallel to the vectorw=6,3,−4?