Diketahui : A = i+3j-2k
B = 5i+j+3k
C =-2i+2j+5k...

Question

Diketahui : A = i+3j-2k
                    B = 5i+j+3k
                    C =-2i+2j+5k
                   Dan titik D pada garis CD       sehingga CD = AB - 3BC
Tentukan :a. Vektor AB +BC
                  b. Panjang AB+BC
                  c. Vektor BD +CD
                  d. panjang BD + CD
                   e. koordinat titik D

Sabrina E · Answer

a. vektor b - vektor a + vektor c - vektor b
    (5,1,3) - (1,3,-2) + (-2,2,5) - (5,1,3)
    (4,-2,5) + (-7,1,2)
    (-3,-1,7)
b. (b - a) + (c -b)
    (4,-2,1) + (-7,1,2)
    (-3,-1,3)

Jaka K · Answer

jawab :
a). AB + BC = ( B - A ) + ( C - B ) 
      • AB = B - A
               = ( 5,1,3 ) - ( 1,3,-2 )
               = ( 4,-2,5 )
      • BC = C - B
               = ( -2,2,5 ) - ( 5,1,3 )
               = ( -7,1,2 )
     maka, vektor AB + BC = ( 4,-2,5 ) + ( -7,1,2 ) = ( -3,-1,7 )

Jaka K · Answer

d). panjang AB ~|AB|
                     =√4²+(-2)²+1²
                     = √16+4+1
                     = √21 
      jawaban : √21

Jaka K · Answer

d). panjang CB ~ |CB|
                      = √(-7)²+1²+2²
                      = √ 49+1+4
                      = √ 54
                      =√ 9×6
                      = 3√6
     jawaban : 3√6

Jaka K · Answer

e). Koordinat titik D :
      CD=AB - 3BC
    D - C = ( B-A ) -3( C-B )
 D - ( -2,2,5 )= ((5,1,3) - (1,3,-2)) -3((-2,2,5)-
                         (5,1,3))
D - (-2,2,5) = (4,-2,5) -3(-7,1,2)
D - (-2,2,5) = (4,-2,5) - (-21,3,6)
D - (-2,2,5) = ( 25,-5,-1)
                D = ( 25,-5,-1) + ( -2,2,5)
                D = ( 23,-3,4 )
jadi koordinat titik D adalah D = ( 23, -3, 4 )

Diketahui : A = i+3j-2k B = 5i+j+3k C =-2i+2j+5k Dan titik D pada garis CD sehingga CD = AB - 3BC Tentukan :a. Vektor AB +BC b. Panjang AB+BC c. Vektor BD +CD d. panjang BD + CD e. koordinat titik D

a. vektor b - vektor a + vektor c - vektor b (5,1,3) - (1,3,-2) + (-2,2,5) - (5,1,3) (4,-2,5) + (-7,1,2) (-3,-1,7) b. (b - a) + (c -b) (4,-2,1) + (-7,1,2) (-3,-1,3)

jawab : a). AB + BC = ( B - A ) + ( C - B ) • AB = B - A = ( 5,1,3 ) - ( 1,3,-2 ) = ( 4,-2,5 ) • BC = C - B = ( -2,2,5 ) - ( 5,1,3 ) = ( -7,1,2 ) maka, vektor AB + BC = ( 4,-2,5 ) + ( -7,1,2 ) = ( -3,-1,7 )

d). panjang AB ~|AB| =√4²+(-2)²+1² = √16+4+1 = √21 jawaban : √21

d). panjang CB ~ |CB| = √(-7)²+1²+2² = √ 49+1+4 = √ 54 =√ 9×6 = 3√6 jawaban : 3√6

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