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Calculus 3 - Vector Projections

  • Thread starter calcphys92
  • Start date
  • #1

Homework Statement


In three dimensions, consider the vector V = a1i + a2j +a3k. Determine the projections of V onto the x, y, z axis.


Homework Equations


These are formulas from my textbook related to projection:

All underscores mean subscript.

Proj_A B = (B * A/|A|) A/|A| = ((B * A)/(A * A)) A

B*A = a_1b_1 + a_2b_2 + a_3b_3

Note: The asterisk * in the equation above is the 'dot' used in vector dot products.

PS. Sorry for not using the latex coding to make the equations look nicer. I've used this before and I know how to use the codes but when I submit them the images are broken.

The Attempt at a Solution



I don't think I'm even close but here's what I did:

(B*A / A*A) A = (a_1 / 1) j = a_1i

That's for the x axis. The projection answers for the other axes I get a_2j and a_3k respectively.
 
Last edited:

Answers and Replies

  • #2
tiny-tim
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welcome to pf!

hi calcphys92! welcome to pf! :wink:
Proj_A B = (B * A/|A|) A/|A| = ((B * A)/(A * A)) A

(B*A / A*A) A = (a_1 / 1) j = a_1i

That's for the x axis. The projection answers for the other axes I get a_2j and a_3k respectively.
yes :smile:

but that definition is a bit complicated, and difficult to remember

it's much easier to say that to find the projection on A, use eA, the unit vector in the A direction …

then ProjAB = (B.eA)eA :wink:
 
  • #3
Thanks for the confirmation and advice. Also can you explain to me what the answer actually means? I'm asked "How do you interpret the results?" But I don't exactly know what vector projections actually are. Thanks in advance
 
  • #4
tiny-tim
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I'm asked "How do you interpret the results?"
well, i suppose the projection is the amount of it in that direction

or the three projections are the components that make up the original vector
 

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