Math Insight

Applet: The magnitude and direction of a vector

The blue arrow represents a vector $\vc{a}$. The two defining properties of a vector, magnitude and direction, are illustrated by a red bar and a green arrow, respectively. The length of the red bar is the magnitude $\|\vc{a}\|$ of the vector $\vc{a}$. The green arrow always has length one, but its direction is the direction of the vector $\vc{a}$. The one exception is when $\vc{a}$ is the zero vector (the only vector with zero magnitude), for which the direction is not defined. You can change either end of $\vc{a}$ by dragging it with your mouse. You can also move $\vc{a}$ by dragging the middle of the vector; however, changing the position of the $\vc{a}$ in this way does not change the vector, as its magnitude and direction remain unchanged.

Applet file: vector_magnitude_direction.ggb

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