How Do You Scale a Unit Vector to a Different Length?

[wtee85]

Calculus: Vectors QUICK HELP PLEASE!

Okay so i need a little help.

Heres the problem.

The question asks...

Find a vector that has the same direction as <-2,4,2> but has length 6.

So i Did the |v|= Sqrt( A1^2+A2^2+A3^2)= sqrt(24) which is how you begin to find the unit vector with the same direction. I get stumped on how to find it with length 6. The new vector with the same direction would be... <-2/Sqrt(24), 4/Sqrt(24), 2/Sqrt(24)... but.. what about the length of 6..?

Can anybody help me? What do i do with this length of 6?

... any help would be awesome!

 

[berkeman]

Say you scaled the original vector by the same amount in all 3 dimensions. Which way would the scaled vector point?

 

[wtee85]

Do you just multiply everything by 6, or in your example by 3?

 

[radou]

Do you just multiply everything by 6, or in your example by 3?

Hint: what is the manitude of the unit vector?

 

[wtee85]

The magnitude of the unit vector is sqrt(24) as i stated above. That is sqrt(24) of the original vector.

 

[wtee85]

? Help?

 

[Hargoth]

The magnitude of the unit vector is sqrt(24) as i stated above. That is sqrt(24) of the original vector.

No, it's one. That's why it is called " unit vector". So what do you have to do to get a vector of length 6 pointing in the same direction?

 

[wtee85]

Do u multiply or divide by 6? I am seriously lost as in how to get the new vector which i have found the direction too, to get a length of 6.. I am totally lost. I would assume you multiply by 6, thus it would be length of 6?

 

[Hargoth]

That's right. Think of it as an stick which is one cm long and pointing in some direction - to get a stick with a length of 6 cm and pointing in the same direction, you have to stick six of these sticks together.

 

[wtee85]

Okay so i need to multiply the new vector by 6. That means <a1*6, a2*6,a3*6>? Do u see what i mean?