[SPLIT] Find the vector component w of u orthogonal to v.

[Peterson25]

Can somebody help me with this one? Given the following vectors:

u=<-3,2>
v=<1,6>

"Find the vector component w of u orthogonal to v."

I came up with the solution: w=<-111/37,74/37>

I found the projection of u onto v which equals w1, then I found w2, and then added the w1 and w2 together. I'm not sure if this is the correct way to do it.

Please point me in the right direction?

 

[pka]

Re: [SPLIT] Find the vector component w of u orthogonal to v

u=<-3,2> & v=<1,6>
"Find the vector component w of u orthogonal to v."

The vector that you need to find is:
\(\displaystyle \L w = u - \frac{{u \cdot v}}{{v \cdot v}}v.\)

 

[Peterson25]

Hmm, I worked it out and came up with w=<0,0> and I highly doubt that's right (or if it is right, I'm not sure how?)!

Any thoughts on this?

 

[pka]

\(\displaystyle \L
w = u - \frac{{u \cdot v}}{{v \cdot v}}v = \left\langle {\frac{{ - 120}}{{37}},\frac{{20}}{{37}}} \right\rangle\)

 

[Peterson25]

ODD!

I wonder where I bodged my work...

Now I know where I messed up. Bah!

I forgot that v*v = ||v||^2.

My first answer was almost right, except I should've left out the last step.

Thank you, and sorry for such stupid mistakes as I seem to be prone to them!