Finding length of vector with unknown variable

• cathal84
In summary, the conversation discusses finding the smallest possible length of a vector with an unknown variable. The equation for finding the length of a vector is discussed, and the question of whether it is possible to find the unknown variable is raised. Ultimately, it is determined that the smallest possible value of the unknown variable is the square root of a number, and the conversation ends with clarification on this concept.
cathal84
Member warned that the homework template is required
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

cathal84 said:
Find the smallest possible length of the vector →v .
That is when the sqrt(a^2+b^2+c^2) is minimal.

cathal84 said:
i work out the equation as per normal i get Sqrt(50/21+b^2)
I'd check that again...

cathal84 said:
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 :)

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.

Bipolar Demon said:
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 :)

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

\

edit: got it. sorry, long time

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

Replusz said:
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?

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?

Replusz said:
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

cathal84 said:
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##?

Ray Vickson said:
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.

1. How do you find the length of a vector when an unknown variable is present?

To find the length of a vector with an unknown variable, you can use the Pythagorean theorem, which states that the length of the vector squared is equal to the sum of the squares of its components. Solve for the variable and then take the square root to find the length.

2. Can you provide an example of finding the length of a vector with an unknown variable?

Yes, for example, if we have a vector with components (3, x), we can use the Pythagorean theorem to find the length. Length squared = 3^2 + x^2. If x = 4, then the length squared = 25. Taking the square root, we find that the length is approximately 5.

3. Is it possible to find the length of a vector with more than one unknown variable?

Yes, it is possible to find the length of a vector with multiple unknown variables. You would need to have equations that relate the unknown variables to each other, and then use substitution or elimination to solve for one variable and find the length.

4. Are there any other methods for finding the length of a vector with an unknown variable?

Yes, another method is to use the dot product. The dot product of two vectors is equal to the product of their lengths multiplied by the cosine of the angle between them. If both vectors have an unknown variable, you can solve for the angle using the dot product equation and then find the length using the cosine function.

5. How does finding the length of a vector with an unknown variable relate to real-world applications?

Finding the length of a vector with an unknown variable is a common problem in physics, engineering, and other fields where vector quantities are used. For example, in navigation, the length of a displacement vector with an unknown velocity can be used to determine the distance traveled by a moving object. In construction, the length of a force vector with an unknown magnitude can be used to calculate the amount of weight a structure can support.

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