anonymous
  • anonymous
Given vectors a = [7, 3] and b = [-2, 2], a) Find proj \(\bf _{b} a\) (Already found it; it's [2, -2] b) Resolve vector 'a' in to rectangular components one of which is in the direction of vector b. (this is what i need help with)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
@mukushla @whpalmer4 @dumbcow @kropot72
anonymous
  • anonymous
neat :-)
anonymous
  • anonymous
wats neat lol

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anonymous
  • anonymous
Find the unit vector \(\hat b=\dfrac1{\|\vec{b}\|}\vec{b}=\dfrac1{2\sqrt2}(-2,2)=(-1/\sqrt2,1/\sqrt2)\)
anonymous
  • anonymous
instead of doing the steps and giving me the answer, it'd be better if u just outlined the steps required
anonymous
  • anonymous
Find the projection in the direction of \(\hat{b}\) -- this is exactly the component asked for in (b):$$\DeclareMathOperator{\proj}{proj}\proj\ _{\hat{b}}\vec{a}=(\vec{a}\cdot\hat{b})\hat{b}=\dots$$
anonymous
  • anonymous
The 'other' component is then just \(\vec{a}-\proj\ _{\hat{b}}\vec{a}\)
anonymous
  • anonymous
that's [2, -2]
anonymous
  • anonymous
so a) and b) have the same answer?
anonymous
  • anonymous
|dw:1371545044564:dw|
anonymous
  • anonymous
@genius12 (b) has an additional part i.e. the difference between (7,3) and (2,-2)
anonymous
  • anonymous
so [5, 5] would be the other component
anonymous
  • anonymous
got it. thx

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