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Vector components question?

  • Thread starter fightboy
  • Start date
25
0
"Is it possible for a vector that has nonzero magnitude to have a component in some direction that is equal to zero?"
The answer key said that any vector that has a nonzero magnitude will always have a component of zero length in the direction perpendicular to the vector.

I'm having trouble visualizing this. Why will the vector always have a component of zero length?
If anyone could break this down for me it would be much appreciated!
 

Answers and Replies

gneill
Mentor
20,560
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Imagine a vector rising perpendicularly from a line (any given line). What's the projection of that vector onto the line?

An obvious analogy is the x-y axes of the Cartesian plane. How much "y" lies along the direction of "x"?
 
rude man
Homework Helper
Insights Author
Gold Member
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Draw a vector A on paper. Now, draw a vector B perpendicular to the A vector, both A and B have their startying ends together. Now draw a vector C from the tip of A to the tip of B. You obviously have C = A + B. How small does B have to be so that A = C?
 

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