Perhatikan gambar! 2u−v+3w=...

Pertanyaan

Perhatikan gambar!

$\style{font-size:14px}{2\overrightarrow u-\overrightarrow v+3\overrightarrow w=...}$

Pembahasan Soal:

Ingat kembali perkalian vektor dengan skalar.

$\begin{array}{rcl}ka&=&k\begin{bmatrix}a\\b\end{bmatrix}\\&=&\begin{bmatrix}ka\\kb\end{bmatrix}\end{array}$

Diketahui :

$begin mathsize 14px style u with rightwards arrow on top equals open square brackets table row 3 row 2 end table close square brackets end style$

$begin mathsize 14px style v with rightwards arrow on top equals open square brackets table row 6 row 8 end table close square brackets end style$

$begin mathsize 14px style w with rightwards arrow on top equals open square brackets table row 5 row 7 end table close square brackets end style$

Sehingga, diperoleh perhitungan berikut.

$begin mathsize 14px style 2 u with rightwards arrow on top minus v with rightwards arrow on top plus 3 w with rightwards arrow on top equals 2 open square brackets table row 3 row 2 end table close square brackets minus open square brackets table row 6 row 8 end table close square brackets plus 3 open square brackets table row 5 row 7 end table close square brackets 2 u with rightwards arrow on top minus v with rightwards arrow on top plus 3 w with rightwards arrow on top equals 2 open square brackets table row 3 row 2 end table close square brackets minus open square brackets table row 6 row 8 end table close square brackets plus 3 open square brackets table row 5 row 7 end table close square brackets 2 u with rightwards arrow on top minus v with rightwards arrow on top plus 3 w with rightwards arrow on top equals open square brackets table row 6 row 4 end table close square brackets minus open square brackets table row 6 row 8 end table close square brackets plus open square brackets table row 15 row 21 end table close square brackets 2 u with rightwards arrow on top minus v with rightwards arrow on top plus 3 w with rightwards arrow on top equals open square brackets table row cell 6 minus 6 plus 15 end cell row cell 4 minus 8 plus 21 end cell end table close square brackets 2 u with rightwards arrow on top minus v with rightwards arrow on top plus 3 w with rightwards arrow on top equals open square brackets table row 15 row 17 end table close square brackets end style$

Jadi, hasil dari $2\overrightarrow u-\overrightarrow v+3\overrightarrow w$ adalah $\begin{bmatrix}15\\17\end{bmatrix}$ .

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Difhayanti

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Terakhir diupdate 11 Oktober 2021