Jika p=(−16) dan q=(−42), nilai ∣∣p−q∣∣=....

Pertanyaan

Jika $\overrightarrow p=\begin{pmatrix}-1\\6\end{pmatrix}$ dan $\overrightarrow q=\begin{pmatrix}-4\\2\end{pmatrix}$ , nilai $\left|\overrightarrow p-\overrightarrow q\right|=...$ .

$7$
$5 square root of 2$
$5$
$3 square root of 2$
$2 square root of 2$

Pembahasan Soal:

Selisih dua vektor dan panjang vektor pada dua dimensi.

Panjang vektor $a with rightwards arrow on top equals open parentheses a subscript 1 comma space a subscript 2 close parentheses$ dapat dihitung dengan rumus berikut.

$open vertical bar a with rightwards arrow on top close vertical bar equals square root of open parentheses a subscript 1 close parentheses squared plus open parentheses a subscript 2 close parentheses squared end root$

Diketahui $p with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row 6 end table close parentheses$ dan $q with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 2 end table close parentheses$ , akan ditentukan nilai $open vertical bar p with rightwards arrow on top minus q with rightwards arrow on top close vertical bar$ .

Perhatikan perhitungan berikut.

$table attributes columnalign right center left columnspacing 2px end attributes row cell open vertical bar p with rightwards arrow on top minus q with rightwards arrow on top close vertical bar end cell equals cell open vertical bar open parentheses table row cell negative 1 end cell row 6 end table close parentheses minus open parentheses table row cell negative 4 end cell row 2 end table close parentheses close vertical bar end cell row blank equals cell open vertical bar open parentheses table row cell negative 1 minus open parentheses negative 4 close parentheses end cell row cell 6 minus 2 end cell end table close parentheses close vertical bar end cell row blank equals cell open vertical bar open parentheses table row 3 row 4 end table close parentheses close vertical bar end cell row blank equals cell square root of open parentheses 3 close parentheses squared plus open parentheses 4 close parentheses squared end root end cell row blank equals cell square root of 9 plus 16 end root end cell row blank equals cell square root of 25 end cell row cell open vertical bar p with rightwards arrow on top minus q with rightwards arrow on top close vertical bar end cell equals 5 end table$

Jadi, jawaban yang tepat adalah C.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

Y. Fathoni

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Terakhir diupdate 06 Oktober 2021