Exercise 1
Determine the equations of the coordinate axes and the coordinate planes.
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)
XOYÂ Â O = (0, 0, 0)Â Â Â Â = (1, 0, 0)Â Â Â = (0, 1, 0)
z = 0
XOZÂ Â Â 0 = (0, 0, 0)Â Â Â = (1, 0, 0)Â Â Â Â Â Â 
= (0, 0, 1)
y = 0
YOZÂ Â Â Â O = (0, 0, 0)Â Â Â Â = (0, 1, 0)Â Â Â Â Â Â = (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)Â Â Â Â Â B = (0, b, 0)Â Â Â Â Â Â Â 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:
Summarise with AI:
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Nice emma really precise information.. I appreciate u
Hey Raptor! Thanks very much for the positive feedback, very much appreciated!
explains everything for a child or a confused student in their ap maths class who is lost in the more detailed mathematics
Draw all types of polygon and its area and perimeter class 7th NCERT course
I’m just curious if the area between the polygon and the circumscribed circle has a name.
https://www.superprof.co.uk/resources/academic/maths/geometry/plane/orthocenter-centroid-circumcenter-and-incenter-of-a-triangle.html
Draw all types of polygon and its area and perimeter