Let A(2, 1, 1), B(1, 2, 1), and C(1, 1, 2) be three given points. Find i) parametric and symmetric equations of the line through the point A and parallel to the line through the points B and C;

Question

Let  A(2, 1, 1), B(1, 2, 1), and C(1, 1, 2) be three given points. Find  i) parametric and symmetric equations of the line through the point  A and parallel to the line through the points B and C;

Ryan Willis · Accepted Answer

Step 1  Let A(2, 1, 1), B(1, 2, 1,) and C(1, 1, 2) be three given points.  To find parametric and symmetric equations of the line through the point  A and parallel to the line through the points B and C  Step 2  Parametric equations of the line through the point (x1, y1, z1) and parallel to the line through the points (x2, y2, z2) and (x3, y3, z3)  x=x1+t(x3−x2)  y=y1+t(y3−y2)  z=z1+t(z3−z2)  Parametric equations of the line through the point  A(2, 1, 1) and parallel to the line through the points B(1, 2, 1), and C(1, 1, 2)  x=2+t(1−1)y=1+t(1−2)z=1+t(2−1)x=2y=1−tz=1+t  Step 3  Symmetric equations of the line through the point (x1, y1, z1) and parallel to the line through the points (x2, y2, z2) and (x3, y3, z3)  x−x1x3−x2=y−y1y3−y2=z−z1z3−z2  Symmetric equations of the line through the point  A(2, 1, 1) and parallel to the line through the points B(1, 2, 1), and C(1, 1, 2)  x−21−1=y−11−2z−12−1  x−20=y−1−1=z−11

Let A(2,\ 1,\ 1),\ B(1,\ 2,\ 1), and C(1,\

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