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Vector Magnitude

Vector Magnitude in 2D

The magnitude of a vector is the numerical value length that a vector possesses. It is always a positive scalar regardless of direction or angle.

In the simulation below, you can see a vector, of variable length and angle based on the movement of your mouse over the simulation in 2D. As you can see in the simulation regardless of which direction the 2D vector is pointing, whether that be the positive or negative x and y axis, or any angle it is in, the magnitude will always be a positive scalar.

The magnitude (length) of the vector once you know the vector components of the vector can be calculated by the following equation:

\[ |\vec{v}| = \sqrt{v_x^2 + v_y^2 + v_z^2} \]

Let's calculate the magnitude of the vector in the simulation:

\[ |\vec{v}| = \sqrt{24^2 + -7^2 + 0^2} \]

\[ |\vec{v}| = \sqrt{576 + 49 + 0} \]

\[ |\vec{v}| = \sqrt{625} \]

\[ |\vec{v}| = 25 \]

As we can see, the magnitude (length) is 25, just like in the simulation. Note that the x-axis vector component is 24 and the y-axis vector component is -7. Note that the y-axis vector component is negative. This is because the vector is facing the negative direction (downward), having an angle of -16.26 degrees.

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