Finding length of vector with unknown variable

[cathal84]

Finding length of vector with unknown variable.
Purely for study purposes.
Find the smallest possible length of the vector →v .
Let vector V = (-2/3,b,16/7)
Equation for finding length of vector : Sqrt(a^2+b^2+c^2)Question would be quite straight forward had there been no unknown variable but since there is i am quite stuck.
when i work out the equation as per normal i get Sqrt(50/21+b^2)
Is it possible to work out the unknown variable in this question? I don't think it is but please correct me if I'm wrong

 

[Replusz]

Find the smallest possible length of the vector →v .

That is when the sqrt(a^2+b^2+c^2) is minimal.

 

[Replusz]

i work out the equation as per normal i get Sqrt(50/21+b^2)

I'd check that again...

 

[Replusz]

Is it possible to work out the unknown variable in this question? I don't think it is but please correct me if I'm wrong

Yes, you can thus you are wrong :)

 

[Logical Dog]

Well, we had these questions for a level. But it doesent make sense to me.

Dont you mean if length of vector x is Y units, and vector X = (-2/3,b,16/7), thus find the value of b.

Otherwise how.. You must have been given a length for the vector, and then told to find the unknown component.? unless length of vector can also be zero.

 

[Replusz]

Well, we had these questions for a level. But it doesent make sense to me.
Dont you mean if length of vector x is Y units, and vector X = (-2/3,b,16/7), thus find the value of b.
Otherwise how.. You must have been given a length for the vector, and then told to find the unknown component.?

It does make sense, hwever its strange how it doesn't matter what a and c are :)

 

[Logical Dog]

It does make sense, hwever its strange how it doesn't matter what a and c are :)

\

edit: got it. sorry, long time

 

[Replusz]

Only if a=b=c=0 then the length l=sqrt(0)=0, yes. But this wasnt the question

 

[cathal84]

Yes, you can thus you are wrong :)

thanks for your reply, since it is possible to find the unknown variable, could you possibly point me in the right direction on how to do so?

 

[Replusz]

the length is sqrt(a^2+b^2+c^2)=sqrt(somehtin+b^2)
something is a number, like 2 or 5, or ... You miscalculated it though. It is a^2+c^2
Now a root is minimal if the thing inseide it is minmal. So b^2 + something is minimal. So b^2 is minimal
So now, what is b?

 

[cathal84]

the length is sqrt(a^2+b^2+c^2)=sqrt(somehtin+b^2)
something is a number, like 2 or 5, or ... You miscalculated it though. It is a^2+c^2
Now a root is minimal if the thing inseide it is minmal. So b^2 + something is minimal. So b^2 is minimal
So now, what is b?

still struggling with the question, i don't believe i have come across the concept of a minimal root and can't seem to find it in my textbook, is it possible you could explain further? thanks

 

[Ray Vickson]

still struggling with the question, i don't believe i have come across the concept of a minimal root and can't seem to find it in my textbook, is it possible you could explain further? thanks

You are over-thinking the problem. If $b$ is allowed to be any real number whatsoever, what is the smallest possible value of $b^2$?

 

[cathal84]

You are over-thinking the problem. If $b$ is allowed to be any real number whatsoever, what is the smallest possible value of $b^2$?

Ah right, that makes a lot more senses haha thanks Ray and Replusz for your contribution.