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Diketahui vektor u , v dan w tidak nol, jika dan dimana 0 ∘ ≤ α ≤ 9 0 ∘ dan 0 ∘ ≤ β ≤ 9 0 ∘ serta , maka....

Diketahui vektor  dan  tidak nol, jika angle open parentheses v with rightwards arrow on top comma w with rightwards arrow on top close parentheses equals alpha dan angle open parentheses u with rightwards arrow on top comma w with rightwards arrow on top close parentheses equals beta dimana  dan  serta open vertical bar v with rightwards arrow on top minus w with rightwards arrow on top close vertical bar equals open vertical bar u with rightwards arrow on top minus w with rightwards arrow on top close vertical bar comma space open vertical bar v with rightwards arrow on top close vertical bar equals open vertical bar u with rightwards arrow on top close vertical bar, maka....

  1. v with rightwards arrow on top equals w with rightwards arrow on top

  2. u with rightwards arrow on top equals v with rightwards arrow on top

  3. alpha equals 0 degree

  4. beta equals 90 degree

  5. cos space alpha greater than cos space beta

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S. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

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Karena , maka: Sehingga didapat Mengakibatkan

begin mathsize 12px style open vertical bar v with rightwards arrow on top minus w with rightwards arrow on top close vertical bar squared equals open vertical bar u with rightwards arrow on top minus w with rightwards arrow on top close vertical bar squared open vertical bar v with rightwards arrow on top close vertical bar to the power of 2 space end exponent plus open vertical bar w with rightwards arrow on top close vertical bar squared minus 2 open vertical bar v with rightwards arrow on top close vertical bar. open vertical bar w with rightwards arrow on top close vertical bar. cos space alpha equals open vertical bar u with rightwards arrow on top close vertical bar to the power of 2 space end exponent plus open vertical bar w with rightwards arrow on top close vertical bar squared minus 2 open vertical bar u with rightwards arrow on top close vertical bar. open vertical bar w with rightwards arrow on top close vertical bar. cos space beta end style

Karena open vertical bar v with rightwards arrow on top close vertical bar equals open vertical bar u with rightwards arrow on top close vertical bar, maka:

begin mathsize 12px style open vertical bar u with rightwards arrow on top close vertical bar to the power of 2 space end exponent plus open vertical bar w with rightwards arrow on top close vertical bar squared minus 2 open vertical bar v with rightwards arrow on top close vertical bar. open vertical bar w with rightwards arrow on top close vertical bar. cos space alpha equals open vertical bar u with rightwards arrow on top close vertical bar to the power of 2 space end exponent plus open vertical bar w with rightwards arrow on top close vertical bar squared minus 2 open vertical bar u with rightwards arrow on top close vertical bar. open vertical bar w with rightwards arrow on top close vertical bar. cos space beta minus 2 open vertical bar v with rightwards arrow on top close vertical bar. open vertical bar w with rightwards arrow on top close vertical bar. cos space alpha equals negative 2 open vertical bar u with rightwards arrow on top close vertical bar. open vertical bar w with rightwards arrow on top close vertical bar. cos space beta cos space alpha equals cos space beta end style

Sehingga didapat alpha equals beta
Mengakibatkan u with rightwards arrow on top equals v with rightwards arrow on top

 

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