# Exercises - The Vigenere's Cipher

1. Encode the message "Attack at Dawn" with a Vigenere's cipher, using the keyword "KEY".

2. The Kryptonian alphabet consists of only 5 letters whose frequencies of occurance are shown below:

$$\begin{array}{c|c|c|c|c} A & B & C & D & E\\\hline 0.05 & 0.10 & 0.20 & 0.30 & 0.35 \end{array}$$

If a plaintext Kryptonian message is encoded using a Vigenere's Cipher with keyword "BED", determine the probability that the first and third letters of the message match.

3. Use the dot product to determine which angle is smaller, the angle between the vectors $\begin{pmatrix}-3\\7\end{pmatrix}$ and $\begin{pmatrix}-4\\8\end{pmatrix}$ or the angle between the vectors $\begin{pmatrix}3\\5\end{pmatrix}$ and $\begin{pmatrix}5\\4\end{pmatrix}$.

4. Which two vectors below have the smallest angle between them? (Note, all three vectors have the same length)

1. $(1, 2, 3, 4)$
2. $(2, 1, 3, 4)$
3. $(1, 3, 4, 1)$

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