# Components

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• May 10th 2008, 03:36 AM
NAPA55
Components
Quick question- if I know the magnitude of a certain vector, the coordinates of its tail (as an ordered triple), and that the vector itself is going in the same direction as another vector (given x/y/z coordinates of the other one), how can I find the components of the vector itself?

I got an answer but I don't think it's right because I can swap my values between x/y/z for it to work... but isn't there just 1 answer (only 1 possible x, y, and z component)?
• May 10th 2008, 03:38 AM
Moo
Quote:

Originally Posted by NAPA55
Quick question- if I know the magnitude of a certain vector, the coordinates of its tail (as an ordered triple), and that the vector itself is going in the same direction as another vector (given x/y/z coordinates of the other one), how can I find the components of the vector itself?

I got an answer but I don't think it's right because I can swap my values between x/y/z for it to work... but isn't there just 1 answer (only 1 possible x, y, and z component)?

Hello,

What do you call "same direction" ? Do you have a given example so that it'd be easier to help you ?
• May 10th 2008, 04:22 AM
NAPA55
I'll just make something up, so when I do the actual problems I still have to think lol

- They give the coordinates of the tail
- They give the magnitude
- They say the vector is in the same direction as u = (4, -3, -6)

I guess by direction they mean which way it is is moving (on positive or negative axis)...

From my made up question here, x is a positive direction while y and z are negative, so I guess that means that the vector that I'm finding has to have a positive x value but negative y and z values.
• May 10th 2008, 04:58 AM
TheEmptySet
Quote:

Originally Posted by NAPA55
I'll just make something up, so when I do the actual problems I still have to think lol

- They give the coordinates of the tail
- They give the magnitude
- They say the vector is in the same direction as u = (4, -3, -6)

I guess by direction they mean which way it is is moving (on positive or negative axis)...

From my made up question here, x is a positive direction while y and z are negative, so I guess that means that the vector that I'm finding has to have a positive x value but negative y and z values.

Because I'm boring lets use the tail at (a,b,c)

So a vector with the same direction as (4,,-3,-6) passing through (a,b,c) can be written as

$v=(a,b,c)+t(4,-3,-6)=(4t+a,-3t+b,-6t+c)$

We can find the magnitude

$\sqrt{(4t+a)^2+(-3t+b)^2+(-6t+c)^2}=M$

From here plug in the magnitude for M and solve the quadratic for the value of t and sub back into the original equation.

Good luck.
• May 10th 2008, 06:50 AM
NAPA55
Wouldn't that give 2 values for t, and therefore 2 possible vectors?

I think there's only supposed to be 1 answer.
• May 10th 2008, 01:56 PM
TheEmptySet
Quote:

Originally Posted by NAPA55
Wouldn't that give 2 values for t, and therefore 2 possible vectors?

I think there's only supposed to be 1 answer.

I hope this helps.

A vector with magnitude 5 and its tail at (0,0) in the direction (3,4)

well one possible answer would be the vector 3i +4j, but what is wrong with
-3i-4j these both have the same magnitude, but face the opposite way.

I guess it depends on how they define direction, you may just want to pick the positive one.
• May 10th 2008, 02:57 PM
NAPA55
I did it another way. Does this work?

I took the vector given (the one that mine follows in the same direction). Then I converted it to a unit vector with magnitude 1. I multiplied the unit vector by a scalar of the magnitude given to come up with a new vector.

Then I separated that new vector into components.

Are the components I'm looking for:
a) The x, y, and z values when the vector has the tail at the origin?

or

b) The x, y, and z values of the tip?

I think the tail information is irrelevant.