A dimensional equation is one in which the units of measurement and their powers are used rather than their actual numeric values.
For example, consider an object under constant acceleration:
let u denote its initial velocity
v denote its final velocity
a the acceleration
and t the time between the initial and final points of time.
Then v = u +at
The dimensional equation is
[LT-1] = [LT-1] + [LT-2][T]
L represents a dimension of length
T represents a dimension of time
M, which does not appear here, would represent mass.
Only terms with the same dimensions may be added or subtracted.
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.
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.
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.
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).
Since a triangle is two-dimensional, it cannot have volume.
yes
The location of a point in 3-dimensional space.
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.
An equation in 6 dimensional space!
An ordered pair or coordinates of a point in 2-dimensional space.
It is the equation of a line in 3-dimensional space.
A line, "living" in N-dimensional space, where N is the number of variables.
There can be linear equations with 1, 2, ... variables. Each of these is different since an equation with n variables belongs to n-dimensional space.