Pertanyaan

Dua vektor P = 3 i + 4 j + 5 k dan Q = 5 i + 12 j + 13 k membentuk sudut α .Hitungbesar cos !

Dua vektor $P = 3 i + 4 j + 5 k$ dan $Q = 5 i + 12 j + 13 k$ membentuk sudut $α$ . Hitung besar cos alpha !

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Jawaban terverifikasi

Jawaban

besarcos adalah 0,98 atau apabila dibulatkan sama dengan 1.

besar cos

adalah 0,98 atau apabila dibulatkan sama dengan 1.

Pembahasan

Diketahui : Ditanyakan : Besar cos ? Jawab : Pada perkalian titik antara dua vektor a dan b ( a • b ), berlaku persamaan : Kemudian, nilaicos dapat dihitung : Dengan demikian, besarcos adalah 0,98 atau apabila dibulatkan sama dengan 1.

Diketahui :

Ditanyakan : Besar cos alpha ?

Jawab :

Pada perkalian titik antara dua vektor a dan b (a • b), berlaku persamaan :

Kemudian, nilai cos bold italic alpha dapat dihitung :

$table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards arrow cell space open vertical bar P with rightwards arrow on top close vertical bar space equals space open vertical bar 3 straight i with hat on top space plus space 4 straight j with hat on top space plus space 5 straight k with hat on top close vertical bar end cell row blank equals cell space square root of 3 squared space plus space 4 squared space plus space 5 squared end root end cell row blank equals cell space square root of 9 space plus space 16 space plus space 25 end root end cell row blank equals cell space square root of 50 space equals space 5 square root of 2 end cell row blank blank blank row blank rightwards arrow cell space open vertical bar Q with rightwards arrow on top close vertical bar space equals space open vertical bar 5 straight i with hat on top space plus space 12 straight j with hat on top space plus space 13 straight k with hat on top close vertical bar end cell row blank equals cell space square root of 5 squared space plus space 12 squared space plus space 13 squared end root end cell row blank equals cell space square root of 25 space plus space 144 space plus space 169 end root end cell row blank equals cell space square root of 338 space equals space 13 square root of 2 end cell row blank blank blank row blank rightwards arrow cell space P space times space Q space equals space open parentheses 3 straight i space plus space 4 straight j space plus space 5 straight k close parentheses space times space open parentheses 5 straight i space plus space 12 straight j space plus space 13 straight k close parentheses end cell row blank equals cell space open parentheses 3 straight i space times space 5 straight i close parentheses space plus space open parentheses 4 straight j space times space 12 straight j close parentheses space plus space open parentheses 5 straight k space times space 13 straight k close parentheses end cell row blank equals cell space 15 space plus space 48 space plus space 65 end cell row blank equals cell space 128 end cell row blank blank blank row blank rightwards arrow cell space P with rightwards arrow on top space times space Q with rightwards arrow on top space equals space open vertical bar P with rightwards arrow on top close vertical bar open vertical bar Q with rightwards arrow on top close vertical bar space cos space alpha end cell row cell cos space alpha space end cell equals cell space fraction numerator P with rightwards arrow on top space times Q with rightwards arrow on top over denominator open vertical bar P with rightwards arrow on top close vertical bar open vertical bar Q with rightwards arrow on top close vertical bar end fraction end cell row cell cos space alpha space end cell equals cell space fraction numerator 128 over denominator open parentheses 5 square root of 2 close parentheses space open parentheses 13 square root of 2 close parentheses end fraction end cell row cell cos space alpha space end cell equals cell space bold 0 bold comma bold 98 end cell row cell cos space alpha space end cell equals cell space bold 1 end cell end table$

Dengan demikian, besar cos adalah 0,98 atau apabila dibulatkan sama dengan 1.