Chapters

## Exercise 1

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

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

Determine the equation of the plane that contains the lines:

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

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

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).

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.

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

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

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

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

Determine the equation of the plane that contains the lines:

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

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

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).

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.

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

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.

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

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