Can two vectors have the same projection?

Can two vectors have the same projection?

The projectoin can be the same, if they are equal. When they are not equal, you have two cases: they are colinear: then the two projections are the identity on both, and so different.

Is the projection of u onto v parallel to u?

The vector parallel to v, with magnitude compvu, in the direction of v is called the projection of u onto v and is denoted projvu. Note projvu is a vector and compvu is a scalar. Find the projection of u = i + 2j onto v = i + j.

What is a vector crossed with itself?

Finally, the cross product of any vector with itself is the zero vector (a×a=0). In particular, the cross product of any standard unit vector with itself is the zero vector.

Can you change the look of a projection?

For visualization (doesn’t affect the projection of the underlying layers), once everything is defined you can change the look of the map on the fly in the Data Frame properties. The projection/coordinate system doesn’t need to be the same as the layers, as long as everything is defined.

How are two maps using the same conic projection?

These two maps both use the same Conic Projection. The first uses only one Standard Parallel and the second uses two Standard Parallels. With this projection the difference between the two is dramatic; with others (such as the Lambert Conformal Conic) the difference is not as dramatic.

Is there such a thing as a perfect projection?

There is no one perfect projection and a map maker must choose the one which best suits their needs. The world maps are samples of the results of different attempts to solve the 3D-to-2D problem. For more information about individual projections see the Some Commonly Used Map Projections section.

Can a projection be configured into a coordinate system?

There are dozens of projections available in ArcGIS that can be configured into countless projected coordinate systems. Your choice of a projected coordinate system depends on many factors, including the part of the world you are mapping, the scale of your map, and the purpose of your map.