Diketahui titik K (2, -1, 4), L (-3, 4, -2),

Berikut ini adalah pertanyaan dari lalahclar74 pada mata pelajaran Matematika untuk jenjang Sekolah Menengah Atas

Diketahui titik K (2, -1, 4), L (-3, 4, -2), dan M (1, 1, -3). Panjang vektor 2KL + LM – KM adalah...

Jawaban dan Penjelasan

Berikut ini adalah pilihan jawaban terbaik dari pertanyaan diatas.

$\sf 2\vec{KL}=2.\left(\vec{L}-\vec{K}\right)$ $=2.\left[\left(\begin{array}{ccc}-3\\4\\-2\end{array}\right)-\left(\begin{array}{ccc}2\\-1\\4\end{array}\right)\right]$ $=2.\left(\begin{array}{ccc}-3-2\\4-(-1)\\-2-4\end{array}\right)$ $=2.\left(\begin{array}{ccc}-5\\5\\-6\end{array}\right)$ $=\left(\begin{array}{ccc}-10\\10\\-12\end{array}\right)$

$\sf \vec{LM}=\vec{M}-\vec{L}$ $=\left(\begin{array}{ccc}1\\1\\-3\end{array}\right)-\left(\begin{array}{ccc}-3\\4\\-2\end{array}\right)$ $=\left(\begin{array}{ccc}1-(-3)\\1-4\\-3-(-2)\end{array}\right)$ $=\left(\begin{array}{ccc}4\\-3\\-1\end{array}\right)$

$\sf \vec{KM}=\vec{M}-\vec{K}$ $=\left(\begin{array}{ccc}1\\1\\-3\end{array}\right)-\left(\begin{array}{ccc}2\\-1\\4\end{array}\right)$ $=\left(\begin{array}{ccc}1-2\\1-(-1)\\-3-4\end{array}\right)$ $=\left(\begin{array}{ccc}-1\\2\\-7\end{array}\right)$

$\sf 2\vec{KL}+\vec{LM}-\vec{KM}$ $=\left(\begin{array}{ccc}-10\\10\\-12\end{array}\right)+\left(\begin{array}{ccc}4\\-3\\-1\end{array}\right)-\left(\begin{array}{ccc}-1\\2\\-7\end{array}\right)$ $=\left(\begin{array}{ccc}-10+4-(-1)\\10+(-3)-2\\-12+(-1)-(-7)\end{array}\right)$ $=\left(\begin{array}{ccc}-5\\5\\-6\end{array}\right)$