vector calculus help?

[whig4life]

Find two unit vectors perpendicular to both v = <3, 1, -1> and
w = <0,1, 2>

Don't forget you are asked for unit vectors. Once you have found one of the unit vectors, stop and think about why
it is really easy to nd the second one.

I am highly confused by this, can someone help me? Thank you

 

[Deleted member 4993]

Find two unit vectors perpendicular to both v = <3, 1, -1> and
w = <0,1, 2>

Don't forget you are asked for unit vectors. Once you have found one of the unit vectors, stop and think about why
it is really easy to nd the second one.

I am highly confused by this, can someone help me? Thank you

Which vector operation - produces another vector perpendicular to two other vectors?

 

[whig4life]

Im sorry but you have all the information that I do...

I believe the question has to do with the cross-product.

 

[pka]

Find two unit vectors perpendicular to both v = <3, 1, -1> and w = <0,1, 2>

Consider \(\displaystyle \pm\dfrac{v\times w}{\|v\times w\|}\)

 

[Deleted member 4993]

Now that you know that the answer involves cross-product of two vectors, please tell us

which method of cross-product have you been taught in your class?

 

[whig4life]

Yes, the method I learned is the same used in this video: http://youtu.be/qsgK1d-_8ik

 

[Deleted member 4993]

Yes, the method I learned is the same used in this video: http://youtu.be/qsgK1d-_8ik

So what did you get as answer (refer to pka's post)?

 

[whig4life]

Still working on the magnitude.

The vector length is 3√6 or is it just √54?

The cross product was (3, -6, 3) now just working on magnitude.

 

[Deleted member 4993]

Still working on the magnitude.

The vector length is 3√6 or is it just √54? → those are same 3√6 = √54 and that is the magnitude!

The cross product was (3, -6, 3) now just working on magnitude.

.

 

[whig4life]

so then the answer is -[3/√54, -6/√54, 3/√54] and 3/√54, -6/√54, 3/√54?

 

[Deleted member 4993]

so then the answer is -[3/√54, -6/√54, 3/√54] and 3/√54, -6/√54, 3/√54?

You should check your answer by conducting the dot products (as suggested by the video).

 

[whig4life]

My calculations are showing that my answer is correct. Do you agree?

 

[HallsofIvy]

Yes, although since you have already been told that \(\displaystyle \sqrt{54}= \sqrt{9(6)}= 3\sqrt{6}\), it might be better to simplify your answers:
\(\displaystyle <3/\sqrt{54}, -6/\sqrt{54}, 3/\sqrt{54}>= <1/\sqrt{6}, -2/\sqrt{6}, 1/\sqrt{6}>\).

You could even "rationalize the denominator" if you wish: \(\displaystyle <\sqrt{6}/6, -2\sqrt{6}/6, \sqrt{6}/6>\).