Materials
Question
1. Scalar multiplication
\vec{u} = \left(\begin{matrix}
3 \\
7 \\
4
\end{matrix}\right)
\, What \, is \,\, 5 \cdot \vec{u}
= ?
Solution:
\\[3mm]
\left(\begin{matrix}
5 \cdot 3 \\
5 \cdot 7 \\
5 \cdot 4
\end{matrix}\right)
Answer:
\\[3mm]
\left(\begin{matrix}
15 \\
35 \\
20
\end{matrix}\right)
2. Addition
\left(\begin{matrix}
5 \\
9
\end{matrix}\right)
+
\left(\begin{matrix}
1 \\
7
\end{matrix}\right)
= ?
Solution:
\\[3mm]
\left(\begin{matrix}
5 + 1 \\
1 + 7
\end{matrix}\right)
Answer:
\\[3mm]
\left(\begin{matrix}
7 \\
16
\end{matrix}\right)
3. Find the magnitude of the vector
\vec{u} =
\left(\begin{matrix}
2 \\
3
\end{matrix}\right)
\ \| \mathbf{\vec{u}} \|
= ?
Solution:
\\[3mm]
\sqrt{2^2 + 3^2}
Answer:
\\[3mm]
\sqrt{11} \ or \ 3.31662...