# Thread: [SOLVED] Find scalar ||kv||=4

1. ## [SOLVED] Find scalar ||kv||=4

v = (-1,2,5)

find scalar k such that ||kv||n = 4

First, what does ||k|| mean? Isn't that the distance between the norm of a vector? or the distance between two points?

I've been able to set this up as

square root (k-1)^2 + (k2)^2+ (k5)^2

I cannot solve this however.

2. Originally Posted by thekrown
v = (-1,2,5)

find scalar k such that ||kv||n = 4

First, what does ||k|| mean? Isn't that the distance between the norm of a vector? or the distance between two points?

I've been able to set this up as

square root (k-1)^2 + (k2)^2+ (k5)^2

I cannot solve this however.
What is $\displaystyle n$?

3. Originally Posted by Prove It
What is $\displaystyle n$?
My mistake, there is no n.

It's:

v = (-1,2,5)

find scalar k such that ||kv|| = 4

4. Originally Posted by thekrown
My mistake, there is no n.

It's:

v = (-1,2,5)

find scalar k such that ||kv|| = 4
Ok, this is saying that there is some vector that has magnitude $\displaystyle 4$ and goes in the direction of $\displaystyle \mathbf{v}$. Therefore it is a scalar multiple of $\displaystyle \mathbf{v}$.

So you need to find the magnitude of $\displaystyle \mathbf{v}$ and then figure out what the scale factor $\displaystyle k$ would be if it is magnified to a magnitude of $\displaystyle 4$.

5. So are they saying v (-1,2,5) is already using the scalar factor 4?

I know ||v|| = square root (-1^2 + 2^2 + 5^2) = square root of 30.

I block when the k is introduced.

||kv|| = |k| * ||v|| yes?

My difficulty is going to 4 from the square root of 30.

6. Originally Posted by thekrown
So are they saying v (-1,2,5) is already using the scalar factor 4?

I know ||v|| = square root (-1^2 + 2^2 + 5^2) = square root of 30.

I block when the k is introduced.

||kv|| = |k| * ||v|| yes?
Yes! so your equation is $\displaystyle ||kv||= |k|||v||= 4$.

Since ||v||= 30, that says 30|k|= 4. Can you solve that?

My difficulty is going to 4 from the square root of 30.

7. Originally Posted by HallsofIvy
Yes! so your equation is $\displaystyle ||kv||= |k|||v||= 4$.

Since ||v||= 30, that says 30|k|= 4. Can you solve that?
Also note that since $\displaystyle k$ is a scalar, you don't need the modulus signs.

8. Ah so 30k = 4 is 30*1/7.5.

k = 7.5^-1

9. No.

If $\displaystyle k\sqrt{30} = 4$

then $\displaystyle k = \frac{4}{\sqrt{30}} = \frac{4\sqrt{30}}{30} = \frac{2\sqrt{30}}{15}$.

I understand what you did and my mistake.

Thanks all!

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### given that ||v|| = 3, find all values of k such that ||kv|| = 5

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