1. ## Vectors!!

Hey guys,

This problem about vectors is giving me some trouble. Help would be greatly appreciated.

Let v= <2,3,2> and w= <4,6,5>

a) Find a unit vector that is orthogonal to both v and w.

b) Find the angle formed by vectors v x w and w x v

c) If u= <-1,4,8> find the cosine of the angle formed by vectors u and v x w

Thanks so much!!

2. ## Re: Vectors!!

Originally Posted by blackflag10
Let v= <2,3,2> and w= <4,6,5>
a) Find a unit vector that is orthogonal to both v and w.

b) Find the angle formed by vectors v x w and w x v

c) If u= <-1,4,8> find the cosine of the angle formed by vectors u and v x w
For a) find $\frac{v\times w}{\|v\times w\|}$.

For b) here is a hint: $v\times w= -w\times v$.

c) $\frac{u\cdot(v\times w)}{\|u\|\|v\times w\|}$

3. ## Re: Vectors!!

Originally Posted by Plato
For a) find $\frac{v\times w}{\|v\times w\|}$.

For b) here is a hint: $v\times w= -w\times v$.

c) $\frac{u\cdot(v\times w)}{\|u\|\|v\times w\|}$
OK, I got A and C. I don't know how I did not see that the first time. But for B, would it be 180 degrees? Would they form a straight line?

Thank you so much!

4. ## Re: Vectors!!

Originally Posted by blackflag10
for B, would it be 180 degrees? Would they form a straight line?
That is correct.

Thanks!!

6. ## Re: Vectors!!

Another useful formula when you have two vectors a dot b = |a||b| cos theta