Write the vector in row or column form. Each row or column’s element should correspond to a given dimension in the Euclidean plane to which it belongs. For example, if your vector is "<9, 4, 8, 1>," you are dealing with a four-dimensional vector. The elements, from left to right, correspond the individual elements of the Euclidean space. In typical mathematical terms, these elements may correspond to the axes “x, y, z and t,” respectively.
Decide how you want to truncate the vector. Truncating a vector means removing some of its dimensions. In most cases, when mathematicians talk about truncating a vector, they mean to cut off the end or beginning of it, leaving either the more basic or more higher dimensions. However, you have the freedom to truncate in any way you wish. That is, you can choose which dimensions to keep in the truncated vector. Usually, you make this determination based on practical reasons: delete the needless dimensions in the vector. For example, if you have a four-dimensional vector and you want to graph it in the coordinates corresponding to length and height, you would cut out the “y” and “t” dimensions.
Truncate the vector. Remove the dimensions you have decided that are not needed. Piece the vector back together afterward. For the example, you would delete the elements in the vector corresponding to the “y” and “t” dimensions -- namely “4” and “1” in "<9, 4, 8, 1>." Piecing the vector back together gives you a vector in the “x-z” coordinates, "<9, 8>."