Pertanyaan

Diketahui vektor a = − 2 i + 5 j + 4 k dan vektor b = 4 i + 5 j + 7 k . Panjang proyeksi vektor a pada vektor b sama dengan ...

Diketahui vektor $a = - 2 i + 5 j + 4 k$ dan vektor $b = 4 i + 5 j + 7 k$ . Panjang proyeksi vektor $a$ pada vektor $b$ sama dengan ...

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Panjang vektor , yaitu Jika vektor dan , maka Panjang proyeksi vektor pada vektor dapat ditentukan menggunakan rumus berikut. Berdasarkan konsep di atas, panjang proyeksivektor pada vektor adalah sebagai berikut. Oleh karena itu, jawaban yang tepat adalah C.

Panjang vektor a with rightwards arrow on top equals x i with rightwards arrow on top plus y j with rightwards arrow on top plus z k with rightwards arrow on top , yaitu open vertical bar a with rightwards arrow on top close vertical bar equals square root of x squared plus y squared plus z squared end root

Jika vektor a with rightwards arrow on top equals a subscript 1 i with rightwards arrow on top plus a subscript 2 j with rightwards arrow on top plus a subscript 3 k with rightwards arrow on top dan b with rightwards arrow on top equals b subscript 1 i with rightwards arrow on top plus b subscript 2 j with rightwards arrow on top plus b subscript 3 k with rightwards arrow on top , maka

a with rightwards arrow on top times b with rightwards arrow 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

Panjang proyeksi vektor stack text a end text with rightwards arrow on top pada vektor stack text b end text with rightwards arrow on top dapat ditentukan menggunakan rumus berikut.

$open vertical bar c with rightwards arrow on top close vertical bar equals open vertical bar fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar b with rightwards arrow on top close vertical bar end fraction close vertical bar$

Berdasarkan konsep di atas, panjang proyeksi vektor stack text a end text with rightwards arrow on top pada vektor stack text b end text with rightwards arrow on top adalah sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar c with rightwards arrow on top close vertical bar end cell equals cell open vertical bar fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar b with rightwards arrow on top close vertical bar end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator open parentheses table row cell negative 2 end cell row 5 row 4 end table close parentheses open parentheses table row 4 row 5 row 7 end table close parentheses over denominator square root of 4 squared plus 5 squared plus 7 squared end root end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator negative 2 times 4 plus 5 times 5 plus 4 times 7 over denominator square root of 16 plus 25 plus 49 end root end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator negative 8 plus 25 plus 28 over denominator square root of 90 end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator 45 over denominator 3 square root of 10 end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator 15 over denominator square root of 10 end fraction close vertical bar end cell row blank equals cell 15 over 10 square root of 10 end cell row blank equals cell 3 over 2 square root of 10 end cell end table$

Oleh karena itu, jawaban yang tepat adalah C.

Latihan Bab

Pengertian dan Operasi Vektor I

Operasi Vektor II

Kedudukan Vektor

Aljabar Vektor I