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Diketahui vektor a = i +2 j - x k , b =3 i - 2 j + k c =2 i + j +2 k . Jika a a tegak lurus c c , maka a + b ∙ a - c ( a ⃗ + b ⃗ ) ∙ ( a ⃗ − c ⃗ ) adalah ...

Diketahui vektor a space ⃗ equals i space ̂ plus 2 j space ̂ minus x k space ̂ comma b space ⃗ equals 3 i space ̂ minus 2 j space ̂ plus k space ̂ comma space c space ⃗ equals 2 i space ̂ plus j space ̂ plus 2 k space ̂. Jika  tegak lurus , maka  adalah ...

  1. -4

  2. -2

  3. 0

  4. 2

  5. 4

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F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Pembahasan

Karena tegak lurus , maka Kemudian Sehingga

Karena a with rightwards arrow on top tegak lurus c with rightwards arrow on top, maka

a with rightwards arrow on top bullet c with rightwards arrow on top equals 0  open parentheses i with hat on top plus 2 j with hat on top minus x k with hat on top close parentheses bullet open parentheses 2 i with hat on top plus j with hat on top plus 2 k with hat on top close parentheses equals 0  1 bullet 2 plus 2 bullet 1 plus open parentheses negative x close parentheses bullet 2 equals 0  2 plus 2 minus 2 x equals 0  4 minus 2 x equals 0  2 x equals 4  x equals 2

Kemudian

a with rightwards arrow on top plus b with rightwards arrow on top equals open parentheses i with hat on top plus 2 j with hat on top minus x k with hat on top close parentheses plus open parentheses 3 i with hat on top minus 2 j with hat on top plus k with hat on top close parentheses equals open parentheses i with hat on top plus 2 j with hat on top minus 2 k with hat on top close parentheses plus open parentheses 3 i with hat on top minus 2 j with hat on top plus k with hat on top close parentheses  equals 4 i with hat on top minus k with hat on top    a with rightwards arrow on top minus c with rightwards arrow on top equals open parentheses i with hat on top plus 2 j with hat on top minus x k with hat on top close parentheses minus open parentheses 2 i with hat on top plus j with hat on top plus 2 k with hat on top close parentheses equals open parentheses i with hat on top plus 2 j with hat on top minus 2 k with hat on top close parentheses minus open parentheses 2 i with hat on top plus j with hat on top plus 2 k with hat on top close parentheses  equals negative i with hat on top plus j with hat on top minus 4 k with hat on top

Sehingga

open parentheses a with rightwards arrow on top plus b with rightwards arrow on top close parentheses bullet open parentheses a with rightwards arrow on top minus c with rightwards arrow on top close parentheses equals open parentheses 4 i with hat on top minus k with hat on top close parentheses bullet open parentheses negative i with hat on top plus j with hat on top minus 4 k with hat on top close parentheses equals 4 bullet open parentheses negative 1 close parentheses plus 0 bullet 1 plus open parentheses negative 1 close parentheses bullet open parentheses negative 4 close parentheses  equals negative 4 plus 0 plus 4 equals 0

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