Magnitude of a Vector with Coordinates

Published on September 23, 2026

Linear-Algebra

Learn how to find the magnitude of a vector $\vec{w}$ starting at the origin and ending at the point (12, 2) by applying the distance formula and rounding to the nearest hundredth.

Question

Answer

To find the magnitude of the vector

, we use the coordinates of its terminal point

since it starts at the origin

Step 1: Apply the magnitude formula.
The magnitude of a vector

is given by

Step 2: Simplify the expression.

Step 3: Calculate the numerical value and round to the nearest hundredth.

Rounding to the nearest hundredth gives

Final Answer:

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