Line Problems

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:

Line Exercises

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

Line Exercises

Parametric Form

Linear Solution

Linear Solution

Linear Solution


2

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

Line Exercises

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:

Linear Calculations

Linear Calculations

Plane Equation

The plane that contains point A and line s:

Linear Calculations

Linear Calculations

Plane Equation

Linear Solution


3

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

Line Exercises

Linear Solution


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.

Normal Vectors

Cross Product

Linear Calculations

Linear Solution




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