Last one. But I don't quite understand why it result in this
coolbreeze
last one. The sum of how u and v line up with w separately is the same as how (u+v) lines up with w.
chovedrecht
We didn't talk about the last one, the distributive property
zhengsef
The vector u+v's projection onto the vector w equals u's projection onto w plus v's projection onto w
hesuyouren
The last one
ohmygearbox
We didn't talk about the distributive property.
goldfish
The last property - the inner product with w distributes between u and v.
aabedon
The last one
MashPlant
last one
samalex
The last one makes sense geometrically because the added (u+v, vector addition takes into account the angle(although obvious)) has info of u, v in it. So if we project it before addition separately and add, the result should be the same as adding the vectors and project
notme
We didn't discuss the last property. It makes sense if we examine how differs from <u, w>. The latter is the projection of w onto u, and the former is the projection onto u + v. So obviously how they line up is affected exactly by how much "pull" v has on the projection. And that difference can therefore be added after the projection onto u by adding <v, w>
fullkeyboardalchemist
The last one.
alexz2
the last one
chenruis
The last one. It's pretty easy to understand if the three vectors are in the same direction. If not then just image u and v onto w and it becomes very algebra.
Last one
a "new" inner product on |R^2: <<u,v>> = 2*<u,v>
Last one. But I don't quite understand why it result in this
last one. The sum of how u and v line up with w separately is the same as how (u+v) lines up with w.
We didn't talk about the last one, the distributive property
The vector u+v's projection onto the vector w equals u's projection onto w plus v's projection onto w
The last one
We didn't talk about the distributive property.
The last property - the inner product with w distributes between u and v.
The last one
last one
The last one makes sense geometrically because the added (u+v, vector addition takes into account the angle(although obvious)) has info of u, v in it. So if we project it before addition separately and add, the result should be the same as adding the vectors and project
We didn't discuss the last property. It makes sense if we examine how differs from <u, w>. The latter is the projection of w onto u, and the former is the projection onto u + v. So obviously how they line up is affected exactly by how much "pull" v has on the projection. And that difference can therefore be added after the projection onto u by adding <v, w>
The last one.
the last one
The last one. It's pretty easy to understand if the three vectors are in the same direction. If not then just image u and v onto w and it becomes very algebra.