# Line Problems

### Solutions

1Given the points A = (2, 6, −3) and B = (3, 3, −2), find the points on the line AB which contain at least one zero coordinate.

2Find the equation of the line that passes through the point A = (1, −1, 0) and cuts the lines:

3Find the equation of the line that passes through the point A = (8, 2, 3) and has the direction vector = (0,1,0).

4Find the Cartesian equation of the line that is parallel to the planes: x − 3y + z = 0 and 2x − y + 3z − 5 = 0, and passes through the point A = (2, −1, 5).

## 1

Given the points A = (2, 6, −3) and B = (3, 3, −2), find the points on the line AB which contain at least one zero coordinate.

## 2

Find the equation of the line that passes through the point A = (1, −1, 0) and cuts the lines:

The required line is the intersection of two planes that passes through point A and contains parts of the lines r and s.

The plane that contains point A and line r:

The plane that contains point A and line s:

## 3

Find the equation of the line that passes through the point A = (8, 2, 3) and has the direction vector = (0,1,0).

## 4

Find the Cartesian equation of the line that is parallel to the planes: x − 3y + z = 0 and 2x − y + 3z − 5 = 0, and passes through the point A = (2, −1, 5).

The direction vector of the line is perpendicular to the normal vectors of each plane.