Quick vector question

[bturville]

Let k=3i - 5j + 2k and v= 2i + 2j.

Is it possible to find 2k - 4v? Can you do it, with them both being in different dimensions (ie R^2 and R^3)?

[Collin Li]

No, you cannot. It is like adding a 3x1 matrix with a 2x1 matrix.

[Mao]

can you not assume v is on the i-j plane, and therefore v=2i+2j+0k??

[Collin Li]

Vectors are analogous to matrices. It is not like real numbers and their relationship to complex numbers, where there is an implied . You just can't add them. If you wanted to add them for some practical application, the 2-dimensional vector would have been better off defined in an i-j plane of an i-j-k world (i.e.: with a k component equal to zero). Technically, looking at this with a mathematical viewpoint only, you can't do it.