CONTOH SOAL VEKTOR DAN JAWABAN

Diketahui tiga buah vektor:  

A = i + 2j - k  
B = 4i + 2j + 3k
C = 2j - 3k

Tentukan: 
a. A ∙ ( B × C )  
b. A ∙ ( B + C )
c. A × ( B + C )
 

Pembahasan:
a.  B × C  
= ( 4i + 2j + 3k ) × ( 2j -3k )  
= ( 4i × 2j ) + (4i × (-3k)) + ( 2j × 2j ) + (2j × (-3k)) + ( 3k × 2j ) + (3k × (-3k)) = 8k + 12j - 6i - 6i
 = -12i + 12j + 8k

A ∙ ( B × C )  
= ( i + 2j - k ) ∙ ( -12i + 12j + 8k )  
= ( 1 ∙ (-12)) + ( 2 ∙ 12 ) + ((-1) ∙ (8))  
= -12 + 24 - 8  
  = 4

b.  B + C  
= ( 4i + 2j + 3k ) + ( 2j -3k )  
= 4i + 4j
 
A ∙ ( B + C ) = ( i + 2j - k ) ∙  ( 4i + 4j )  
= ( 1 ∙ 4 ) + ( 2 ∙ 4 ) + ((-1) ∙ 0 )  
= 4 + 8  
= 12
 

c. A × ( B + C )  
= ( i + 2j - k ) × ( 4i + 4j )  
= ( i ∙ 4i ) + ( i ∙ 4j ) + ( 2j ∙ 4i ) + ( 2j ∙ 4j ) + ((-k) ∙ 4i) + ((-k) ∙ 4j)
= 4k - 8k - 4j + 4i
= 4i - 4j - 4k 



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