Question

Find the point of intersection of the line passing through the points $(1,1,-1);(-1,0,1)$ and the xy-plane.

Answer 1

Lets recall the equation of line given 2 points,

$\frac{x-x_1}{x_2-x_1}=$$\frac{y-y_1}{y_2-y_1}=$$\frac{z-z_1}{z_2-z_1}$

here we have $(x_1,y_1,z_1)=(1,1,-1)$ $(x_2,y_2,z_2)=(-1,0,1)$

We have the equation of line as,

$\frac{x-1}{-2}=$$\frac{y-1}{-1}=$$\frac{z+1}{2}$

Point on the line can be written as $(-2p+1,-p+1,2p-1)$

Now to find intersection with xy plane we put z=0,

$2p-1=0,p=1/2$

Point of intersection after putting $p$ is $(0,1/2,0)$