Chapters

## Exercise 1

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

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## Exercise 2

Determine the equation of the plane that contains the lines:

## Exercise 3

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

## Exercise 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 .

## Exercise 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).

## Exercise 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.

## Exercise 7

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

## Exercise 8

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

## Exercise 9

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

## Solution of exercise 1

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

x - axis           O = (0, 0, 0)              = (1, 0, 0)

y - axis           O = (0, 0, 0)            (0, 1, 0)

z - axis          O (0, 0, 0)              = (0, 0, 1)

XOY   O = (0, 0, 0)        = (1, 0, 0)      = (0, 1, 0)

z = 0

XOZ     0 = (0, 0, 0)      = (1, 0, 0)            = (0, 0, 1)

y = 0

YOZ       O = (0, 0, 0)        = (0, 1, 0)            = (0, 0, 1)

x = 0

## Solution of exercise 2

Determine the equation of the plane that contains the lines:

-2x + 3y + 7z + 14 = 0

## Solution of exercise 3

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

## Solution of exercise 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 .

## Solution of exercise 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).

## Solution of exercise 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.

A = (a, 0, 0)          B = (0, b, 0)              C = (0, 0, c)

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

## Solution of exercise 7

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

## Solution of exercise 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.

## Solution of exercise 9

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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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.