anonymous
  • anonymous
Find two unit vectors that make an angle of 60° with v = ‹6, 8›. Give your answers correct to three decimal places.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
v*x = |v||x| cos 60
anonymous
  • anonymous
x/|x| = (|v| cos 60 )/v
anonymous
  • anonymous
i know \[\left| v \right|\] = 10 but im not for sure on the rest

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anonymous
  • anonymous
|v|cos 60 = 5 5/v = <5/6, 5/8 > but |<5/6, 5/8 >| does not quite equal 1 so Im tripping
anonymous
  • anonymous
no it doesnt...1.04
anonymous
  • anonymous
converting v to unit vector...
anonymous
  • anonymous
Let u = ha, bi be a unit vector. By Theorem 3 we need u·v = |u| |v| cos 60◦ ⇔ 4a + 3b = (1)(5) 1 2 ⇔ b = 5 2·3 − 4 3a. Since u is a unit vector, |u| = √a2 + b2 = 1 ⇔ a2 +b2 = 1 ⇔ a2 + 􀀀5 6 − 4 3a2 = 1 ⇔ ⇔ 100a2 − 80a − 11 = 0. By the quadratic formula, a = −(−80) ±p(−80)2 − 4(100)(−11) 2(100) = 80 ± √10800 200 . If a = 20 + √2700 25 ≈ 0.92 then b = 5 6 − 4 3 (0.919615) ≈ −0.393 , and if a = 20 − √2700 25 ≈ −0.12 then b = 5 6 − 4 3 (−0.119615) ≈ 0.993 . Thus the two unit vectors are h0.92,−0.393i and h−0.12, 0.993i.
anonymous
  • anonymous
this was with <4,3>
anonymous
  • anonymous
I crashed :( let me check my latest
anonymous
  • anonymous
lol...ok
anonymous
  • anonymous
<5/6, 5/8> is sooo close, Im thinking precision error :)
anonymous
  • anonymous
1.0416666...
anonymous
  • anonymous
so then what is the other vector?
anonymous
  • anonymous
so v hat is <3/5,4/5> then v*x = |v||x| cos 60 becomes v*x = cos 60
anonymous
  • anonymous
for the other vector flip the y axis, cos 60 = cos -60

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