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Vector Magnitude

Vector Magnitude in 1D x-axis

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. As you can see in the simulation regardless of which direction the vector is pointing, whether that be the positive or negative x-axis, or any angle it is in, 0 or 180, 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:

\[ |\vec{v}| = \sqrt{-16.7^2 + 0^2 + 0^2} \]

\[ |\vec{v}| = \sqrt{278.89 + 0 + 0} \]

\[ |\vec{v}| = \sqrt{278.89} \]

\[ |\vec{v}| = 16.7 \]

As we can see, the magnitude (length) is 16.7, just like in the simulation. Note that the x-axis vector component is also 16.7, however in this case negative. This is because the vector is on the x-axis only, facing the negative direction, and having an angle of 180 degrees.

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