Unit7 - Lines and Planes in 3-D Linear Equations In 2-D Ax By = C What is the graph In 3-D Ax By Cz = D What is the graph Review Parametric Equations

Unit7 - Lines and Planes in 3-D Linear Equations In 2-D Ax...

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Lines and Planes in 3-D Linear Equations: In 2-D: Ax + By = C What is the graph? D What is the graph? Review Parametric Equations General 2-D: Example: x = f ( t ) y = g ( t ) x = t 2 y = 4 t 2 What about 3-D?
Lines in 3-D Given: P 1 ( x 1 , y 1 , z 1 ) is a specific point on the line v = a , b , c is 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 : . ? ?

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