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

prelimaf1

prelimaf1

Answered question

2021-12-07

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;

Answer & Explanation

Ryan Willis

Ryan Willis

Beginner2021-12-08Added 15 answers

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(x3x2)
y=y1+t(y3y2)
z=z1+t(z3z2)
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(11)y=1+t(12)z=1+t(21)x=2y=1tz=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)
xx1x3x2=yy1y3y2=zz1z3z2
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)
x211=y112z121
x20=y11=z11

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