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Jika a = 3 i − 5 k dan b = − 2 i + j ​ − k , maka proyeksi skalar 2 a pada b = ....

Jika  dan , maka proyeksi skalar  pada

  1. begin mathsize 14px style negative 1 over 6 square root of 6 end style 

  2. begin mathsize 14px style negative 1 third square root of 6 end style 

  3. begin mathsize 14px style 1 third square root of 6 end style 

  4. begin mathsize 14px style 1 over 6 square root of 6 end style 

  5. begin mathsize 14px style square root of 6 end style 

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Pembahasan

Diketahui vektor dan , maka : Misal adalah proyeksi skalar pada , maka :

Diketahui vektor  begin mathsize 14px style straight a with rightwards arrow on top equals 3 straight i with rightwards arrow on top minus 5 straight k with rightwards arrow on top end style dan begin mathsize 14px style straight b with rightwards arrow on top equals negative 2 straight i with rightwards arrow on top plus straight j with rightwards arrow on top minus straight k with rightwards arrow on top end style, maka :

begin mathsize 14px style 2 straight a with rightwards arrow on top equals 2 open parentheses 3 straight i with rightwards arrow on top minus 5 straight k with rightwards arrow on top close parentheses equals 6 straight i with rightwards arrow on top minus 10 straight k with rightwards arrow on top end style 

Misal begin mathsize 14px style straight c with rightwards arrow on top end style adalah proyeksi skalar begin mathsize 14px style 2 straight a with rightwards arrow on top end style pada undefined, maka :

begin mathsize 14px style straight c with rightwards arrow on top equals fraction numerator 2 straight a with rightwards arrow on top space. space straight b with rightwards arrow on top over denominator open vertical bar straight b with rightwards arrow on top close vertical bar end fraction equals fraction numerator open parentheses 6 straight i with rightwards arrow on top minus 10 straight k with rightwards arrow on top close parentheses space. space open parentheses negative 2 straight i with rightwards arrow on top plus straight j with rightwards arrow on top minus straight k with rightwards arrow on top close parentheses over denominator square root of open parentheses negative 2 close parentheses squared plus 1 squared plus open parentheses negative 1 close parentheses squared end root end fraction equals fraction numerator negative 12 plus 0 plus 10 over denominator square root of 6 end fraction equals negative fraction numerator 2 over denominator square root of 6 end fraction cross times fraction numerator square root of 6 over denominator square root of 6 end fraction equals negative 2 over 6 square root of 6 equals negative 1 third square root of 6 end style 

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Proyeksi skalar a = ⎝ ⎛ ​ − 2 m 2 ​ ⎠ ⎞ ​ pada b = ⎝ ⎛ ​ − 2 1 − 2 ​ ⎠ ⎞ ​ adalah 3 4 ​ . Nilai m = ....

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