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Diketahui u dan v vektor tak nol sembarang, w=∣v∣u+∣u∣v. Jika θ=∠(u, w) dan ϕ=∠(v, w) maka...

Pertanyaan

Diketahui top enclose u dan top enclose v vektor tak nol sembarang, top enclose w equals open vertical bar top enclose v close vertical bar top enclose u plus open vertical bar top enclose u close vertical bar top enclose v. Jika theta equals angle left parenthesis top enclose u comma space top enclose w right parenthesis dan ϕ equals angle left parenthesis top enclose v comma space w right parenthesis maka...

  1. ϕ minus theta equals 90 degree 

  2. ϕ plus theta equals 90 degree 

  3. ϕ equals theta 

  4. theta minus ϕ equals 90 degree 

  5. ϕ plus theta equals 180 degree 

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Ingat kembali rumus berikut.

  • cos space theta equals fraction numerator top enclose a bullet top enclose b over denominator open vertical bar top enclose a close vertical bar open vertical bar top enclose b close vertical bar end fraction  
  • top enclose u bullet top enclose u equals open vertical bar top enclose u close vertical bar squared 

Diketahui theta equals angle left parenthesis top enclose u comma space top enclose w right parenthesis.

Akan ditentukan cos space theta 

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space theta end cell equals cell fraction numerator top enclose u bullet top enclose w over denominator open vertical bar top enclose u close vertical bar open vertical bar top enclose w close vertical bar end fraction end cell row blank equals cell fraction numerator top enclose u bullet left parenthesis open vertical bar top enclose v close vertical bar top enclose u plus open vertical bar top enclose u close vertical bar top enclose v right parenthesis over denominator open vertical bar top enclose u close vertical bar open vertical bar top enclose w close vertical bar end fraction end cell row blank equals cell fraction numerator open vertical bar top enclose v close vertical bar top enclose u times top enclose u plus open vertical bar top enclose u close vertical bar top enclose v times top enclose u over denominator open vertical bar top enclose u close vertical bar open vertical bar top enclose w close vertical bar end fraction end cell row blank equals cell fraction numerator open vertical bar top enclose v close vertical bar open vertical bar top enclose u close vertical bar squared plus open vertical bar top enclose u close vertical bar top enclose v space top enclose u over denominator open vertical bar top enclose u close vertical bar open vertical bar top enclose w close vertical bar end fraction end cell row blank equals cell fraction numerator open vertical bar top enclose v close vertical bar open vertical bar top enclose u close vertical bar plus top enclose v space top enclose u over denominator open vertical bar top enclose w close vertical bar end fraction end cell row blank blank blank end table  

Diketahui ϕ equals angle left parenthesis top enclose v comma space w right parenthesis.

Akan ditentukan cos space ϕ 

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space ϕ end cell equals cell fraction numerator top enclose v bullet top enclose w over denominator open vertical bar top enclose v close vertical bar open vertical bar top enclose w close vertical bar end fraction end cell row blank equals cell fraction numerator top enclose v bullet left parenthesis open vertical bar top enclose v close vertical bar top enclose u plus open vertical bar top enclose u close vertical bar top enclose v right parenthesis over denominator open vertical bar top enclose v close vertical bar open vertical bar top enclose w close vertical bar end fraction end cell row blank equals cell fraction numerator open vertical bar top enclose v close vertical bar top enclose v space top enclose u plus open vertical bar top enclose u close vertical bar top enclose v space top enclose v space over denominator open vertical bar top enclose v close vertical bar open vertical bar top enclose w close vertical bar end fraction end cell row blank equals cell fraction numerator open vertical bar top enclose v close vertical bar top enclose v space top enclose u plus open vertical bar top enclose u close vertical bar open vertical bar top enclose v close vertical bar squared over denominator open vertical bar top enclose v close vertical bar open vertical bar top enclose w close vertical bar end fraction end cell row blank equals cell fraction numerator top enclose v space top enclose u plus open vertical bar top enclose u close vertical bar open vertical bar top enclose v close vertical bar over denominator open vertical bar top enclose w close vertical bar end fraction end cell row blank equals cell fraction numerator open vertical bar top enclose v close vertical bar open vertical bar top enclose u close vertical bar plus top enclose v space top enclose u over denominator open vertical bar top enclose w close vertical bar end fraction end cell row blank blank blank row blank blank blank end table 

Perhatikan bahwa 

cos space theta equals cos space ϕ equals fraction numerator open vertical bar top enclose v close vertical bar open vertical bar top enclose u close vertical bar plus top enclose v space top enclose u over denominator open vertical bar top enclose w close vertical bar end fraction 

Jadi space theta equals ϕ.

Oleh karena itu, jawaban yang benar adalah C.

1rb+

5.0 (8 rating)

Nabila aurelia

Pembahasan lengkap banget

Tricahyanti

Ini yang aku cari!

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