A dimensional check in an equation can provide a quick check about the possible correctness of the equation. For example, if you are supposed to calculate a speed, the dimensions of the result MUST be of the form [distance] / [time] (or something that you can simplify to distance/time). If it doesn't, the formula is wrong. If it does, it MIGHT be correct.
Yes.
The first step in describing the figure that results from the intersection of a plane with a three-dimensional figure is to identify the equation of the plane and the equation of the three-dimensional figure. Next, you need to determine the points where the plane intersects the three-dimensional figure by substituting the plane's equation into the figure's equation. This will produce a new equation representing the intersection, which can then be analyzed to identify the resulting geometric shape.
An ordered pair or coordinates of a point in 2-dimensional space.
A line, "living" in N-dimensional space, where N is the number of variables.
It is the equation of a line in 3-dimensional space.
Yes.
It is a linear equation in two dimensional space. Such an equation defines a line in 2-d
A solution (in 2-dimensional space).A solution (in 2-dimensional space).A solution (in 2-dimensional space).A solution (in 2-dimensional space).
The location of a point in 3-dimensional space.
Since a triangle is two-dimensional, it cannot have volume.
yes
Dimensional analysis simply ensures that two sides of an equation have the same dimensions. By "dimensions" I mean quantities like distance, pressure, force, time, electric charge, etc. For example, a distance can not equal a time. So, if the dimensions are wrong, the equation is wrong, but if the dimensions are right, the equation may be right or it may be wrong. Getting the dimensions right is only part of the task!
An equation in 6 dimensional space!
An ordered pair or coordinates of a point in 2-dimensional space.
3 dimensional geometry.3 dimensional geometry.3 dimensional geometry.3 dimensional geometry.
A line, "living" in N-dimensional space, where N is the number of variables.
It is the equation of a line in 3-dimensional space.