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anonymous

  • 4 years ago

Find two unit vectors that make an angle of 60° with v = ‹6, 8›. Give your answers correct to three decimal places.

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  1. anonymous
    • 4 years ago
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    v*x = |v||x| cos 60

  2. anonymous
    • 4 years ago
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    x/|x| = (|v| cos 60 )/v

  3. anonymous
    • 4 years ago
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    i know \[\left| v \right|\] = 10 but im not for sure on the rest

  4. anonymous
    • 4 years ago
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    |v|cos 60 = 5 5/v = <5/6, 5/8 > but |<5/6, 5/8 >| does not quite equal 1 so Im tripping

  5. anonymous
    • 4 years ago
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    no it doesnt...1.04

  6. anonymous
    • 4 years ago
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    converting v to unit vector...

  7. anonymous
    • 4 years ago
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    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.

  8. anonymous
    • 4 years ago
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    this was with <4,3>

  9. anonymous
    • 4 years ago
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    I crashed :( let me check my latest

  10. anonymous
    • 4 years ago
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    lol...ok

  11. anonymous
    • 4 years ago
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    <5/6, 5/8> is sooo close, Im thinking precision error :)

  12. anonymous
    • 4 years ago
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    1.0416666...

  13. anonymous
    • 4 years ago
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    so then what is the other vector?

  14. anonymous
    • 4 years ago
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    so v hat is <3/5,4/5> then v*x = |v||x| cos 60 becomes v*x = cos 60

  15. anonymous
    • 4 years ago
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    for the other vector flip the y axis, cos 60 = cos -60

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