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Pertanyaan

Jika P(2,1,2) , A(9,-6,2) dan B(2,-4,7), maka sudut antara P A ⇀ dan PB ⇀ adalah ....

Jika P(2,1,2) , A(9,-6,2) dan B(2,-4,7), maka sudut antara dan adalah ....

  1. 0 to the power of straight o

  2. 30 to the power of straight o

  3. 45 to the power of straight o

  4. 60 to the power of straight o

  5. 90 to the power of straight o

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Rumus sudut antara dua vektor dixcari dengan

stack P A with rightwards harpoon with barb upwards on top equals A minus P equals left parenthesis 9 comma negative 6 comma 2 right parenthesis minus left parenthesis 2 comma 1 comma 2 right parenthesis equals left parenthesis 7 comma negative 7 comma 0 right parenthesis stack P B with rightwards harpoon with barb upwards on top equals B minus P equals left parenthesis 2 comma negative 4 comma 7 right parenthesis minus left parenthesis 2 comma 1 comma 2 right parenthesis equals left parenthesis 0 comma negative 5 comma 5 right parenthesis

 

stack P A with rightwards harpoon with barb upwards on top. stack P B with rightwards harpoon with barb upwards on top equals left parenthesis 7.0 plus left parenthesis negative 7 right parenthesis left parenthesis negative 5 right parenthesis plus 0.5 right parenthesis equals 35

open vertical bar stack P A with rightwards harpoon with barb upwards on top close vertical bar equals square root of 7 squared plus left parenthesis negative 7 right parenthesis squared plus 0 squared end root equals 7 square root of 2 open vertical bar stack P B with rightwards harpoon with barb upwards on top close vertical bar equals square root of 0 squared plus left parenthesis negative 5 right parenthesis squared plus 5 squared end root equals 5 square root of 2

 

Rumus sudut antara dua vektor dixcari dengan

cos space theta equals fraction numerator stack P A with rightwards harpoon with barb upwards on top. stack P B with rightwards harpoon with barb upwards on top over denominator open vertical bar stack P A with rightwards harpoon with barb upwards on top close vertical bar open vertical bar stack P B with rightwards harpoon with barb upwards on top close vertical bar end fraction cos space theta equals fraction numerator 35 over denominator open parentheses 7 square root of 2 close parentheses open parentheses 5 square root of 2 close parentheses end fraction cos space theta equals 35 over 70 cos space theta equals 1 half theta equals 60 to the power of straight o

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