Vectors allow you to represent quantities with both size and direction, such as the velocity of an airplane. Better yet, they do so in a mathematically-useful way. Dive in to see how!

Given the vectors

\[\begin{align} \vec{a} &=(1, -4),\\ \vec{b} &=(2, 3),\\ \vec{p} &=-\vec{a}+3\vec{b},\\ \vec{q} &=2\vec{a}-5\vec{b}, \end{align}\]

what is \(2\vec{p}-4\vec{q}?\)

What real values of \(x\) and \(y\) satisfy the equation \[ x(1,2)-y(2,3)=(5, 3)? \]

Which of the following is the same vector as \(\vec{c}\) in the regular hexagon below?

\[\]
**Details and assumptions**

- Let \(\vec{AB}=\vec{a},\) \(\vec{AC}=\vec{b},\) \(\vec{AF}=\vec{c}.\)

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