panjang vektor dari hasil penjumlahan
Jawaban:
C. 11
Penjelasan dengan langkah-langkah:
[tex]\boxed{\bold{\large{\textit{VECTOR}}}}[/tex]
[tex]\vec{a} + \vec{b} = \boxed{\left(\begin{aligned} a_1 \\ a_2 \\ a_3 \end{aligned} \right) + \left(\begin{aligned} b_1 \\ b_2 \\ b_3 \end{aligned} \right) = \left(\begin{aligned} a_1 & + b_1 \\ a_2 & + b_2 \\ a_3 & + b_3 \end{aligned} \right)}[/tex]
[tex]\vec{a} - \vec{b} = \boxed{\left(\begin{aligned} a_1 \\ a_2 \\ a_3 \end{aligned} \right) - \left(\begin{aligned} b_1 \\ b_2 \\ b_3 \end{aligned} \right) = \left(\begin{aligned} a_1 & - b_1 \\ a_2 & - b_2 \\ a_3 & - b_3 \end{aligned} \right)}[/tex]
Diketahui:
- vector a = (6, -4, 5)
- vector b = (3, 2, 1)
Ditanya:
- panjang vector dari hasil a + b?
Jawab:
[tex]\vec{a} + \vec{b} = \left(\begin{aligned} 6 & + 3 \\ -4 & + 2 \\ 5 & + 1 \end{aligned} \right) = \left(\begin{aligned} 9 \\ -2 \\ 6 \end{aligned} \right)[/tex]
panjang vector:
[tex]\begin{aligned} |v| & = \sqrt{a^2 + b^2 + c^2} \\ & = \sqrt{9^2 + (-2)^2 + 6^2} \\ & = \sqrt{81 + 4 + 36} \\ & = \sqrt{121} \\ & = 11 \end{aligned}[/tex]
Jawaban: 11
Semoga membantu ^_^
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