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Jika a = 3 i − 2 j ​ + k dan b = − 3 i + j ​ − 4 k , maka: (1) ∣ ∣ ​ a + b ∣ ∣ ​ = 10 ​ (2) ∣ ∣ ​ a ∣ ∣ ​ : ∣ ∣ ​ b ∣ ∣ ​ = 1 : 2 (3) a ⋅ b = − 15 (4) a sejajar b Pernyataan yang benar adalah ...

Jika  dan , maka: 

(1)  
(2)  
(3)  
(4)  sejajar  

Pernyataan yang benar adalah ...

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L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

pernyataan yang benar adalah dan

pernyataan yang benar adalah open parentheses 1 close parentheses dan open parentheses 3 close parentheses

Pembahasan

Diketahui dan (1) (2) (3) (4) sejajar Dengan demikian, pernyataan yang benar adalah dan

Diketahui a with rightwards arrow on top equals 3 i with rightwards arrow on top minus 2 j with rightwards arrow on top plus k dan b with rightwards arrow on top equals negative 3 i with rightwards arrow on top plus j with rightwards arrow on top minus 4 k with rightwards arrow on top

(1) open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar equals square root of 10  

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top plus b with rightwards arrow on top end cell equals cell open parentheses 3 i with rightwards arrow on top minus 2 j with rightwards arrow on top plus k with rightwards arrow on top close parentheses plus open parentheses negative 3 i with rightwards arrow on top plus j with rightwards arrow on top minus 4 k with rightwards arrow on top close parentheses end cell row blank equals cell open parentheses negative j with rightwards arrow on top minus 3 k with rightwards arrow on top close parentheses end cell row blank blank cell maka space end cell row cell open vertical bar a with italic rightwards arrow on top plus b with italic rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses negative 1 close parentheses squared plus open parentheses negative 3 close parentheses squared end root end cell row blank equals cell square root of 1 plus 9 end root end cell row blank equals cell square root of 10 end cell row blank blank blank end table 

(2) open vertical bar a with rightwards arrow on top close vertical bar space colon space open vertical bar b with rightwards arrow on top close vertical bar equals 1 space colon space 2

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses 3 close parentheses squared plus open parentheses negative 2 close parentheses squared plus open parentheses 1 close parentheses squared end root end cell row blank equals cell square root of 9 plus 4 plus 1 end root end cell row blank equals cell square root of 14 end cell row blank blank blank row cell open vertical bar b with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses negative 3 close parentheses squared plus open parentheses 1 close parentheses squared plus open parentheses negative 4 close parentheses squared end root end cell row blank equals cell square root of 9 plus 1 plus 16 end root end cell row blank equals cell square root of 26 end cell row blank blank cell maka space end cell row cell open vertical bar a with rightwards arrow on top close vertical bar space colon space open vertical bar b with rightwards arrow on top close vertical bar end cell equals cell square root of 14 space colon space square root of 26 end cell end table 


(3) a with rightwards arrow on top times b with rightwards arrow on top equals negative 15 

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals cell open parentheses 3 i with rightwards arrow on top minus 2 j with rightwards arrow on top plus k with rightwards arrow on top close parentheses times open parentheses negative 3 i with rightwards arrow on top plus j with rightwards arrow on top minus 4 k with rightwards arrow on top close parentheses end cell row blank equals cell open parentheses negative 9 close parentheses plus open parentheses negative 2 close parentheses plus open parentheses negative 4 close parentheses end cell row blank equals cell negative 15 end cell end table 


(4) a with rightwards arrow on top sejajar b with rightwards arrow on top

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals cell negative 15 end cell row blank blank blank row cell open vertical bar a with rightwards arrow on top close vertical bar times open vertical bar b with rightwards arrow on top close vertical bar end cell equals cell square root of 14 times square root of 26 end cell row blank equals cell square root of 224 end cell row blank blank blank row cell Karena space open vertical bar a with rightwards arrow on top close vertical bar times open vertical bar b with rightwards arrow on top close vertical bar end cell not equal to cell a with rightwards arrow on top times b with rightwards arrow on top comma space maka space a with rightwards arrow on top space d a n space b with rightwards arrow on top space tidak space sejajar end cell end table 


Dengan demikian, pernyataan yang benar adalah open parentheses 1 close parentheses dan open parentheses 3 close parentheses

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