Drawing Vectors in 1D

A vector in one dimension has both magnitude (size) and direction. We draw vectors as arrows:

• Length shows magnitude
• Arrow shows direction

To correctly describe a vector, you must specify both:

• Magnitude: How large the vector is (always a positive number)
• Direction: Which way the vector points (indicated by + or - sign)

For example, saying "a vector of 5" is incomplete. You must say "a vector of magnitude 5 in the positive direction" or, in 1D, write it as $\vec{x} = +5$.

In 1D, we choose which direction is positive. Usually:

• Horizontal: positive is rightward, negative is leftward
• Vertical: positive is upward, negative is downward

For example, if we define rightward as positive, then $\vec{x} = +5$ has magnitude 5 units and points in the positive (rightward) direction. When drawing it, the arrow extends 5 units to the right.

Key principle: Arrow length must match magnitude. A vector with twice the magnitude needs an arrow twice as long.

A vector $\vec{x} = -8$ has magnitude 8 units and points in the negative (leftward) direction. When drawing it, the arrow extends 8 units to the left. It would be twice as long as $\vec{x} = -4$, which has magnitude 4 units but points in the same direction.

Vectors in the vertical direction: The same principles apply when vectors point up or down. If we define upward as positive, then positive vectors point up and negative vectors point down.