Determine if two vectors are orthogonal

Hey everyone! I have a question about the orthogonality of two vectors

The question is: It is given: **llmll = 4**; **llnll = square root of 3**; **(m^,n)= 150 degrees**

(i) find the norm of the vector m + 2n

(ii) Determine if the vectors (m+2n) and (-m+n) are orthogonal

I got an answer of 2 for the norm but I don't know what to do for the second part. Do I just substitute the values of m and n into the vectors and if they both equal 0 when multiplied, they are orthogonal? Any help would be greatly appreciated :)

Re: Determine if two vectors are orthogonal

Quote:

Originally Posted by

**hemster83** Hey everyone! I have a question about the orthogonality of two vectors

The question is: It is given: **llmll = 4**; **llnll = square root of 3**; **(m^,n)= 150 degrees**

(i) find the norm of the vector m + 2n

(ii) Determine if the vectors (m+2n) and (-m+n) are orthogonal

What does the notation **(m^,n)= 150 degrees** mean?

I have never seem that used.

Re: Determine if two vectors are orthogonal

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Originally Posted by

**Plato** What does the notation **(m^,n)= 150 degrees** mean?

I have never seem that used.

It means the angle between m and n equals 150 degrees. I think my prof made it up himself

Re: Determine if two vectors are orthogonal

Quote:

Originally Posted by

**hemster83** It means the angle between m and n equals 150 degrees. I think my prof made it up himself

**How very odd is that?**

Quote:

Originally Posted by

**hemster83** The question is: It is given: **llmll = 4**; **llnll = square root of 3**; **(m^,n)= 150 degrees**

(i) find the norm of the vector m + 2n

(ii) Determine if the vectors (m+2n) and (-m+n) are orthogonal

Well you know that $\displaystyle \frac{{m \cdot n}}{{\left\| m \right\|\left\| n \right\|}} = \cos \left( {\frac{{5\pi }}{6}} \right) = \frac{{ - \sqrt 3 }}{2}$.

From that you can find $\displaystyle m\cdot n~.$

Now $\displaystyle \|m+2n\|^2=(m+2n)\cdot(m+2n)=m\cdot m+4(n\cdot m)+4(n\cdot n)~.$

Re: Determine if two vectors are orthogonal

I have this same exact question.

Quote:

Well you know that $\displaystyle \frac{{m \cdot n}}{{\left\| m \right\|\left\| n \right\|}} = \cos \left( {\frac{{5\pi }}{6}} \right) = \frac{{ - \sqrt 3 }}{2}$.

From that you can find $\displaystyle m\cdot n~.$

Now $\displaystyle \|m+2n\|^2=(m+2n)\cdot(m+2n)=m\cdot m+4(n\cdot m)+4(n\cdot n)~.$

Now this is the method I used to find the norm, or length of the vector (m+2n). However, I am still at a loss as to how to test the orthogonality of the two vectors (m+2n) and (-m+n).

Thanks in advance.

Re: Determine if two vectors are orthogonal

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Originally Posted by

**Kristoffermk3** I have this same exact question.

Now this is the method I used to find the norm, or length of the vector (m+2n). However, I am still at a loss as to how to test the orthogonality of the two vectors (m+2n) and (-m+n).

What is $\displaystyle (m+2n)\cdot(-m+n)=~?$

Re: Determine if two vectors are orthogonal

Yes, that's what i'm looking for.

I suppose the part that is confusing me is simply that its not asking something as simple as (m dot n). Which is very simple to figure out, but I am confused on how to approach this when they are combinations of vectors such as (m+2n) and (-m+n)...

Re: Determine if two vectors are orthogonal

Quote:

Originally Posted by

**Kristoffermk3** Yes, that's what i'm looking for.

I suppose the part that is confusing me is simply that its not asking something as simple as (m dot n). Which is very simple to figure out, but I am confused on how to approach this when they are combinations of vectors such as (m+2n) and (-m+n)...

$\displaystyle (m+2n)\cdot(-m+n)=-m\cdot m-2 m\cdot n+m\cdot n+2n\cdot n$

Re: Determine if two vectors are orthogonal

Oh my, that seems so self-evident now. (Headbang)

Thank you very much for your clarification.