Question

Find the projection of u onto v. Then write u as the sum of two orthogonal vectors, one
of which is projvu .
1. u = <3, –4>
v = <2, 1>

Answer 1

Do you remember the formula for projection?

Answer 2

no

Answer 3

thats why i don't know how to solve the problem

Answer 4

The unit vector of the one being projected on, times the comp

Answer 5

ok thanks :D

Answer 6

Do you know the comp?

Answer 7

lol i will figure it out

Answer 8

It is the dot product divided by the magnitude of he vector being projected onto

Answer 9

\[
\text{proj}_\mathbf{v}\mathbf{u}=\text{comp}_\mathbf{v}\mathbf{u}\frac{\mathbf{v}}{||\mathbf{v}||} = \frac{\mathbf{v}\cdot \mathbf{u}}{||\mathbf{v}||}\frac{\mathbf{v}}{||\mathbf{v}||} = \frac{\mathbf{v}\cdot \mathbf{u}}{||\mathbf{v}||^2}\mathbf{v} = \frac{\mathbf{v}\cdot \mathbf{u}}{\mathbf{v}\cdot \mathbf{v}}\mathbf{v}
\]

Answer 10

never mind. i was doing the wrong homework. no wonder i didn't understand it