Thread: [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.

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 ?

Originally Posted by Prove It

What is ?

My mistake, there is no n.

It's:

v = (-1,2,5)

find scalar k such that ||kv|| = 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 and goes in the direction of . Therefore it is a scalar multiple of .


So you need to find the magnitude of and then figure out what the scale factor would be if it is magnified to a magnitude of .

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.

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 .

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

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

Originally Posted by HallsofIvy

Yes! so your equation is .

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

Also note that since is a scalar, you don't need the modulus signs.

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

k = 7.5^-1

No.

If

then .

*smacks forehead*. Yes the square root... I had jumped ahead and forgot about the square root.

I understand what you did and my mistake.

Thanks all!