If you intend 'dimensions' to mean units then whenever the two quantities are to be operated on each other then they must have the 'dimensions', refer to dimensional analysis
Two lines intersect at one point. If in two dimensions, and they do not intersect they are parallel. The other option in two dimensions is they are the co-linear, that is they are the same line, in which case they intersect at all points.
yes
The area of a rectangle is equal to its length times its width. So any two rectangles for which these dimensions have the same product, the area is the same. For example, a rectangle that is two meters wide and three meters long and one that is one meter wide and six meters long will both have an area of six square meters.
They must be the same length.
A plane has two dimensions, length and width.
No
Yes.
Yes they must be in the same units of measurements.
No, it is not true.
Same direction and equal magnitudes.
The answer will depend on (a) whet the dimensions of the two quantities are, and (b) what the missing operator between the two quantities is.
Yes, always. One molecule plus one atom is not 2 of anything. One unit north plus one unit east is not 2 units northeast. ■
No. Measurement units are defined by and conversely. So the same units necessarily means same dimensions.
Yes, you can have two objects with identical masses by either having two objects made from the same material and dimensions or by adjusting the quantities of different materials to have the same mass.
Scaling is when you multiply or divide two quantities by the same number.
True-
For two tables made from the same wood to be identical, they must have the same dimensions, shape, design, finish, and overall construction techniques. Additionally, factors like the type of wood, grain pattern, and color should also be consistent between the two tables.