Plane Problems

Solutions

1Determine the equations of the coordinate axes and the coordinate planes.

2Determine the equation of the plane that contains the lines:

3Determine the equation of the plane that contains the point A = (2, 5, 1) and the line:

4Find the intersecting point between the plane x + 2y − z − 2 = 0, the line determined by the point (1, −3, 2) and the vector .

5Determine, in intercept form, the equation of the plane that passes through the points A = (2, 0, 0), B = (0, 4, 0) and C = (0, 0, 7).

6π is a plane that passes through P = (1, 2, 1) and intersects the positive coordinate semi-axes at points A, B and C. If ABC is an equilateral triangle, determine the equations of π.

7Find the equation of the plane that passes through the point P = (1, 1, 1) and is parallel to:

8Determine the equation of the plane that contains the line and is parallel to the line .

9Calculate the equation of the plane that passes through the point (1, 1, 2) and is parallel to the following lines:

1

Determine the equations of the coordinate axes and the coordinate planes.

2

Determine the equation of the plane that contains the lines:

3

Determine the equation of the plane that contains the point A = (2, 5, 1) and the line:

4

Find the intersecting point between the plane x + 2y − z − 2 = 0, the line determined by the point (1, −3, 2) and the vector .

5

Determine, in intercept form, the equation of the plane that passes through the points A = (2, 0, 0), B = (0, 4, 0) and C = (0, 0, 7).

6

π is a plane that passes through P = (1, 2, 1) and intersects the positive coordinate semi-axes at points A, B and C. If ABC is an equilateral triangle, determine the equations of π.

As the triangle is equilateral, the three line segments are equal.

7

Find the equation of the plane that passes through the point P = (1, 1, 1) and is parallel to:

8

Determine the equation of the plane that contains the line and is parallel to the line .

The point A = (2, 2, 4) and the vector belong to the plane because the line is in the plane.

The vector is a vector in the plane because it is parallel to the line.

9

Calculate the equation of the plane that passes through the point (1, 1, 2) and is parallel to the following lines: