Help me Find a Vector of Length 6 with Same Direction!

In summary, the problem is to find a vector with the same direction as <-2,4,2> but with length 6. The process to find a unit vector with the same direction is to use the formula |v|=Sqrt(A1^2+A2^2+A3^2)=sqrt(24). However, the question is unsure of how to find the vector with length 6. The solution is to simply multiply the unit vector by 6, as the purpose of unit vectors is to make calculations easier.
  • #1
wtee85
8
0
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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!
 
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  • #2
You simply multiply your last vector by six. Because your last vector has the length of one, you would get a vector of length six just by simply multiplying your vector by 6. That's the whole point of unit vectors. They make calculations really easy. :biggrin:
 
  • #3
Why the same post two times?
 

1. How do I find a vector of length 6 with the same direction?

To find a vector of length 6 with the same direction, you can use the scalar multiplication property. Simply multiply any vector with a magnitude of 1 by 6 to get a vector with the same direction and a magnitude of 6.

2. Can any vector have the same direction as a vector of length 6?

Yes, any vector can have the same direction as a vector of length 6 as long as it is multiplied by a scalar value of 6.

3. How can I determine the direction of a vector?

The direction of a vector can be determined by calculating its angle with the x-axis. This angle is typically measured counterclockwise and can be found using trigonometric functions such as sine and cosine.

4. Is a vector of length 6 always in the same direction as a vector of length 1?

No, a vector of length 6 is not always in the same direction as a vector of length 1. The direction of a vector also depends on its components and can vary depending on the values of those components.

5. Can I use a graph to find a vector of length 6 with the same direction?

Yes, you can use a graph to find a vector of length 6 with the same direction. By plotting the vector on a graph and scaling it to a length of 6, you can determine its direction and use the scalar multiplication property to find a vector with the same direction and a magnitude of 6.

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