# vectors clarification?

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#1
in my textbook, "a position vector of the point relative to the centre of mass" is denoted as r', and they also state r = R + r'. Im having trouble mapping this out on a general 3d space, and also confused on what the meaning of "relative to" is. Can anybody help me on this?
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8 months ago
#2
(Original post by poop yakuza)
in my textbook, "a position vector of the point relative to the centre of mass" is denoted as r', and they also state r = R r'. Im having trouble mapping this out on a general 3d space, and also confused on what the meaning of "relative to" is. Can anybody help me on this?
A vector is just a displacement in n dimensional space. It can start anywhere. In the case above, r' starts at the centre of mass (it's a displacement relative to there), with r and R being defined as starting at the origin. You can now draw a triangle with sides of r, R (from O to the CoM) and r'.

The vectors themselves don't have a starting point, but their values implicitly assume one from their definition.
Last edited by RogerOxon; 8 months ago
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#3
(Original post by RogerOxon)
A vector is just a displacement in n dimensional space. It can start anywhere. In the case above, r' starts at the centre of mass (it's a displacement relative to there), with r and R being defined as starting at the origin. You can now draw a triangle with sides of r, R (from O to the CoM) and r'.

The vectors themselves don't have a starting point, but their values implicitly assume one from their definition.
Would it look something like this?
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8 months ago
#4
(Original post by poop yakuza)
Would it look something like this?
Almost. Check the directions of r and r'.

From your equation, you should see that following R then r' in their indicated directions, should take you to the same point as r does, both from O.
Last edited by RogerOxon; 8 months ago
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#5
(Original post by RogerOxon)
Almost. Check the directions of r and r'.

From your equation, you should see that following R then r' in their indicated directions, should take you to the same point as r does, both from O.

I’ve corrected it (I misread r = R + r’)
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8 months ago
#6
(Original post by poop yakuza)

I’ve corrected it (I misread r = R + r’)
That's it!
1
#7
(Original post by RogerOxon)
That's it!
absolute goat!
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