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## Properties of a Vector

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!

# Vector Addition

Two vectors $$\vec{a}$$, $$\vec{b}$$ are shown in the diagram above. Which of the following is the same vector as $$\vec{a}+ \vec{b}$$?

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 $$\vec{AB}=\vec{a},$$ $$\vec{AC}=\vec{b},$$ $$\vec{AF}=\vec{c}.$$

Two vectors $$\vec{a}$$, $$\vec{b}$$ are shown in the diagram above. Which of the following is the same vector as $$\vec{a}- \vec{b}$$ ?

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