Roboguru

Jika nilai  dan tangen sudut antara vektor  dan  adalah  , hasil  adalah ....

Pertanyaan

Jika nilai vertical line u with rightwards harpoon with barb upwards on top vertical line equals 6 comma space vertical line v with rightwards harpoon with barb upwards on top vertical line equals 10 comma dan tangen sudut antara vektor u with rightwards harpoon with barb upwards on top dan v with rightwards harpoon with barb upwards on top adalah 4 over 3 , hasil u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top adalah ....

Pembahasan Soal:

Untuk menentukan hasil u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top, kita bisa gunakan rumus 

cos space alpha equals fraction numerator u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top over denominator open vertical bar u with rightwards harpoon with barb upwards on top close vertical bar open vertical bar v with rightwards harpoon with barb upwards on top close vertical bar end fraction 

Diketahui: tan space alpha equals 4 over 3 

tan space alpha equals depan over samping  

Menentukan sisi miring, dengan Pythagoras.

Misalkan: r adalah sisi miring.

table attributes columnalign right center left columnspacing 0px end attributes row r equals cell square root of 4 squared plus 3 squared end root end cell row blank equals cell square root of 16 plus 9 end root end cell row blank equals cell square root of 25 end cell row blank equals 5 end table  

Sehingga, cosinus sudut antara vektor u with rightwards harpoon with barb upwards on top dan v with rightwards harpoon with barb upwards on top:

cos space alpha equals samping over miring equals 3 over 5  

Menentukan hasil u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top.

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space alpha end cell equals cell fraction numerator u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top over denominator open vertical bar u with rightwards harpoon with barb upwards on top close vertical bar open vertical bar v with rightwards harpoon with barb upwards on top close vertical bar end fraction end cell row cell 3 over 5 end cell equals cell fraction numerator u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top over denominator 6 times 10 end fraction end cell row cell 3 over 5 end cell equals cell fraction numerator u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top over denominator 60 end fraction end cell row cell 5 open parentheses u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top close parentheses end cell equals cell 3 times 60 end cell row cell 5 open parentheses u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top close parentheses end cell equals 180 row cell u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top end cell equals cell 180 over 5 end cell row cell u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top end cell equals 36 end table 

Jadi, hasil u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top adalah 36.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Juni 2021

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