Vector Exercises Part 2

Normalization of Vectors

Normalize the following vectors

$A=\left[\begin{array}{c}4 \\ -3\end{array}\right]$
$A=\left[\begin{array}{c}-6 \\ 7\end{array}\right]$
$C=12.5@25.5$

Dot Product

Calculate the Dot Product of the following pairs of vectors.

$A=\left[\begin{array}{c}2 \\ -5\end{array}\right]$ and $B=\left[\begin{array}{c}-3 \\ 6\end{array}\right]$
$C=\left[\begin{array}{c}-5 \\ 1\end{array}\right]$ and $D=\left[\begin{array}{c}-4 \\ 1\end{array}\right]$
$E=10@10.5$ and $F=5@105.5$

Angle between Vectors

Calculate the angle between each of the following pairs of vectors (the Dot Products were calculated previously):

$A=\left[\begin{array}{c}2 \\ -5\end{array}\right]$ and $B=\left[\begin{array}{c}-3 \\ 6\end{array}\right]$
$C=\left[\begin{array}{c}-5 \\ 1\end{array}\right]$ and $D=\left[\begin{array}{c}-4 \\ 1\end{array}\right]$
$E=10@10.5$ and $F=5@105.5$

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