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Diketahui : a ⇀ = i + 2 ​ j dan b ⇀ = i − 2 ​ j Hitunglah: Besar sudut kedua vektor (misalkan θ )

 Diketahui :  dan  

Hitunglah: Besar sudut kedua vektor (misalkan )

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R. RGFLLIMA

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Pembahasan

Diketahui : Sudutantar dua vektor adalah : Jadii, Besar sudut kedua vektor adalah .

Diketahui :

straight a with rightwards harpoon with barb upwards on top equals straight i plus square root of 2 straight j straight a with rightwards harpoon with barb upwards on top equals open parentheses table row 1 row cell square root of 2 end cell end table close parentheses straight b with rightwards harpoon with barb upwards on top equals straight i minus square root of 2 straight j straight b with rightwards harpoon with barb upwards on top equals open parentheses table row 1 row cell negative square root of 2 end cell end table close parentheses

Sudut antar dua vektor adalah :

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space straight theta end cell equals cell fraction numerator straight a with rightwards harpoon with barb upwards on top times straight b with rightwards harpoon with barb upwards on top over denominator open vertical bar straight a with rightwards harpoon with barb upwards on top close vertical bar times open vertical bar straight b with rightwards harpoon with barb upwards on top close vertical bar end fraction end cell row blank equals cell fraction numerator left parenthesis 1 right parenthesis left parenthesis 1 right parenthesis plus left parenthesis square root of 2 right parenthesis left parenthesis negative square root of 2 right parenthesis end root over denominator square root of 1 squared plus left parenthesis square root of 2 right parenthesis squared end root times square root of 1 squared plus left parenthesis negative square root of 2 right parenthesis squared end root end fraction end cell row blank equals cell fraction numerator 1 minus 2 over denominator square root of 3 times square root of 3 end fraction end cell row blank equals cell negative 1 third end cell row straight theta equals cell cos to the power of negative 1 end exponent left parenthesis negative 1 third right parenthesis end cell row blank equals cell 109 comma 47 degree end cell end table  

Jadii, Besar sudut kedua vektor adalah 109 comma 47 degree.

 

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