Question

Find the parametric equations for the line that passes through the points P (1,1,0) and Q (0,2,2).

Answer 1

Answer:

The parametric equations for the given line are x=1-t, y=1+t and z=2t.

Step-by-step explanation:

Given information: P (1,1,0) and Q (0,2,2).

The parametric equation of line are

$x=x_0+at$

$y=y_0+bt$

$z=z_0+ct$

where, $(x_0,y_0,z_0)$ is point on line and <a,b,c> is direction vector.

The line passes through the points P (1,1,0) and Q (0,2,2). So, the direction vector is

$\overrightarrow{v}=$

$\overrightarrow{v}=$

$\overrightarrow{v}=$

The direction vector is <-1,1,2>. So, a=-1, b=1 and c=2. The parametric equation of line are

$x=1+(-1)t=1-t$

$y=1+(1)t=1+t$

$z=0+(2)t=2t$

Therefore the parametric equations for the given line are x=1-t, y=1+t and z=2t.