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Pertanyaan

Diketahui a with rightwards harpoon with barb upwards on top equals 4 i plus j plus 5 k dan b with rightwards harpoon with barb upwards on top equals 2 i plus j minus 5 k 

a. a with rightwards harpoon with barb upwards on top plus b with rightwards harpoon with barb upwards on top 

b. a with rightwards harpoon with barb upwards on top minus b with rightwards harpoon with barb upwards on top 

c. a with rightwards harpoon with barb upwards on top minus 2 b with rightwards harpoon with barb upwards on top 

d. 2 a with rightwards harpoon with barb upwards on top times 3 b with rightwards harpoon with barb upwards on top 

S. Nur

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Jawaban terverifikasi

Jawaban

hasil yang diperoleh adalah a with rightwards harpoon with barb upwards on top plus b with rightwards harpoon with barb upwards on top equals 6 i plus 2 ja with rightwards harpoon with barb upwards on top minus b with rightwards harpoon with barb upwards on top equals 2 i plus 10 k dan 2 a with rightwards harpoon with barb upwards on top times 3 b with rightwards harpoon with barb upwards on top equals negative 96.

Pembahasan

Diketahui a with rightwards harpoon with barb upwards on top equals 4 i plus j plus 5 k dan b with rightwards harpoon with barb upwards on top equals 2 i plus j minus 5 k 

a. Ingat kembali jika a with rightwards harpoon with barb upwards on top equals a subscript 1 i plus a subscript 2 j plus a subscript 3 k dan b with rightwards harpoon with barb upwards on top equals b subscript 1 i plus b subscript 2 j plus b subscript 3 k maka a with rightwards harpoon with barb upwards on top plus b with rightwards harpoon with barb upwards on top equals left parenthesis a subscript 1 plus b subscript 1 right parenthesis i plus left parenthesis a subscript 2 plus b subscript 2 right parenthesis j plus left parenthesis a subscript 3 plus b subscript 3 right parenthesis k 

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards harpoon with barb upwards on top plus b with rightwards harpoon with barb upwards on top end cell equals cell left parenthesis 4 plus 2 right parenthesis i plus left parenthesis 1 plus 1 right parenthesis j plus left parenthesis 5 plus left parenthesis negative 5 right parenthesis right parenthesis k end cell row blank equals cell 6 i plus 2 j end cell end table 

Jadi, a with rightwards harpoon with barb upwards on top plus b with rightwards harpoon with barb upwards on top equals 6 i plus 2 j.

b. Ingat kembali bahwa jika a with rightwards harpoon with barb upwards on top equals a subscript 1 i plus a subscript 2 j plus a subscript 3 k dan b with rightwards harpoon with barb upwards on top equals b subscript 1 i plus b subscript 2 j plus b subscript 3 k maka a with rightwards harpoon with barb upwards on top minus b with rightwards harpoon with barb upwards on top equals left parenthesis a subscript 1 minus b subscript 1 right parenthesis i plus left parenthesis a subscript 2 minus b subscript 2 right parenthesis j plus left parenthesis a subscript 3 minus b subscript 3 right parenthesis k 

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards harpoon with barb upwards on top minus b with rightwards harpoon with barb upwards on top end cell equals cell left parenthesis 4 minus 2 right parenthesis i plus left parenthesis 1 minus 1 right parenthesis j plus left parenthesis 5 minus left parenthesis negative 5 right parenthesis k end cell row blank equals cell 2 i plus 10 k end cell end table 

Jadi, a with rightwards harpoon with barb upwards on top minus b with rightwards harpoon with barb upwards on top equals 2 i plus 10 k.

c. Ingat kembali bahwa misalkan k adalah bilangan skalar dan a with rightwards harpoon with barb upwards on top equals a subscript 1 i plus a subscript 2 j plus a subscript 3 k maka  k a with rightwards harpoon with barb upwards on top equals k a subscript 1 i plus k a subscript 2 k plus k a subscript 3 k 

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards harpoon with barb upwards on top minus 2 b with rightwards harpoon with barb upwards on top end cell equals cell left parenthesis 4 i plus j plus 5 k right parenthesis minus left parenthesis 2 left parenthesis 2 i plus j minus 5 k right parenthesis right parenthesis end cell row blank equals cell left parenthesis 4 i plus j plus 5 k right parenthesis minus left parenthesis 4 i plus 2 j minus 10 k right parenthesis end cell row blank equals cell left parenthesis 4 minus 4 right parenthesis i plus left parenthesis 1 minus 2 right parenthesis j plus left parenthesis 5 minus left parenthesis negative 10 right parenthesis right parenthesis k end cell row blank equals cell negative j plus 15 k end cell end table 

Jadi, a with rightwards harpoon with barb upwards on top minus 2 b with rightwards harpoon with barb upwards on top equals negative j plus 15 k.

d. Ingat kembali bahwa jika a with rightwards harpoon with barb upwards on top equals a subscript 1 i plus a subscript 2 j plus a subscript 3 k dan b with rightwards harpoon with barb upwards on top equals b subscript 1 i plus b subscript 2 j plus b subscript 3 k maka a with rightwards harpoon with barb upwards on top times b with rightwards harpoon with barb upwards on top equals a subscript 1 times b subscript 1 plus a subscript 2 times b subscript 2 plus a subscript 3 times b subscript 3 

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a with rightwards harpoon with barb upwards on top times 3 b with rightwards harpoon with barb upwards on top end cell equals cell 2 left parenthesis 4 comma space 1 comma space 5 right parenthesis times 3 left parenthesis 2 comma space 1 comma space minus 5 right parenthesis end cell row blank equals cell left parenthesis 8 comma space 2 comma space 10 right parenthesis times left parenthesis 6 comma space 3 comma space minus 15 right parenthesis end cell row blank equals cell 8 times 6 plus 2 times 3 plus 10 times negative 15 end cell row blank equals cell 48 plus 6 minus 150 end cell row blank equals cell 54 minus 150 end cell row blank equals cell negative 96 end cell end table 

Jadi, 2 a with rightwards harpoon with barb upwards on top times 3 b with rightwards harpoon with barb upwards on top equals negative 96.

Dengan demikian, hasil yang diperoleh adalah a with rightwards harpoon with barb upwards on top plus b with rightwards harpoon with barb upwards on top equals 6 i plus 2 ja with rightwards harpoon with barb upwards on top minus b with rightwards harpoon with barb upwards on top equals 2 i plus 10 k dan 2 a with rightwards harpoon with barb upwards on top times 3 b with rightwards harpoon with barb upwards on top equals negative 96.

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