anonymous
  • anonymous
the symbol\[A _{b}\] stands for the projection of vector A onto vector B. In other words, \[A _{b}\] represents the component of A that is parallel to B. Derive an expression for \[A _{b}\] in terms of the vectors A and B.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
\[\frac{a.b}{|a|^2}a\]
anonymous
  • anonymous
wow u did that really quickly
amistre64
  • amistre64
just got out of calc3 that just went over it :)

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anonymous
  • anonymous
in the numerator...is that a times b?
amistre64
  • amistre64
a dot b
anonymous
  • anonymous
a dot b divided by magnitude of a squared all multiplied by a?
amistre64
  • amistre64
yes, the left side is a scalar; and the right side is vector a scaled to that length
anonymous
  • anonymous
would it be a bother to run me through how u got to this expression?
amistre64
  • amistre64
|dw:1327527260794:dw|
amistre64
  • amistre64
|b| cos(t) = the length of Ab, if we use your notation for proj{a} b
amistre64
  • amistre64
\[|b|cos(t) =|b| \frac{a.b}{|a||b|}=\frac{a.b}{|a|}\] good so far?
anonymous
  • anonymous
yea i get that
anonymous
  • anonymous
i'm with u
anonymous
  • anonymous
i'm also trying to decode your picture :)
anonymous
  • anonymous
is that the x coordinate down there at the end?
anonymous
  • anonymous
the long vector
amistre64
  • amistre64
now, we need to scale that to a unit vector of a; since a is |a| long, lets divide it by |a| to get it to a length of 1
amistre64
  • amistre64
\[\frac{a.b}{|a|}\ \frac{a}{|a|}=; unit\ a, scaled\ by\ needed\ length\]
anonymous
  • anonymous
okay
amistre64
  • amistre64
and since |a| |a| = |a|^2 i just condensed it alittle bit
anonymous
  • anonymous
simple enough?
amistre64
  • amistre64
|dw:1327527605851:dw|
anonymous
  • anonymous
can u redraw that picture from above?
anonymous
  • anonymous
oh okay now i see
amistre64
  • amistre64
lol, i cant draw on this thing very well period :)
anonymous
  • anonymous
okay....so that's it for the equation now?
amistre64
  • amistre64
to find the the vector that is the proj of b onto a; yes; reduce a to ints unit equivalent; and scale it up by the magnitude of b*cos(t)
anonymous
  • anonymous
and what u first initally gave me is that correct?
amistre64
  • amistre64
yes, seeing how that is what we ended up with in the end i would say that its correct :)
anonymous
  • anonymous
u are an absolute life saver
amistre64
  • amistre64
thnx, good luck :)

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