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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 Terminology

Which of the following is a vector quantity?

1. The displacement from New York to London
2. The color of a shoe
3. The number of books on a shelf
4. An array with the number of books reads by each student in a class
5. The speed of an airplane

Which of the following vectors in the regular hexagon below has the same magnitude as $$\vec{AB}$$ but opposite direction?

 Details and assumptions:

• O is the intersection point of the three diagonal lines.

If $$\vec{a}=\vec{b},$$ which of the following is/are true?

I. $$\vec{a}$$ and $$\vec{b}$$ are parallel.
II. $$\vec{a}$$ and $$\vec{b}$$ are equal in magnitude.
III. The initial points of $$\vec{a}$$ and $$\vec{b}$$ are the same.
IV. The terminal points of $$\vec{a}$$ and $$\vec{b}$$ are the same.

Let $$\vec{OA}=\vec{a}+2\vec{b}, \vec{OB}=3\vec{a}-\vec{b},$$ and $$\vec{OC}=2\vec{a}+k\vec{b}$$ in the diagram below. If the three points $$A, B,$$ and $$C$$ lie on the line $$l$$, which of the following is equal to $$k$$?

 Details and assumptions:

• Point $$O$$ does $$\color{red}{\text{not}}$$ lie on the line $$l.$$

Find the unit vector in the direction $$(1,2,3).$$

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