How to find magnitude of a vector

General
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how to find magnitude of a vector

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How to find the magnitude of a vector

Answer:
To find the magnitude of a vector, you can follow these steps:

  1. Understand what a vector is: A vector is a mathematical object that has both magnitude and direction. It is often represented by an arrow in space.

  2. Determine the components: If the vector is given in component form as (a, b) or [a, b], these are the x and y components of the vector in a two-dimensional space.

  3. Use the Pythagorean theorem: To find the magnitude of the vector with components (a, b), you can use the formula |\vec{v}| = \sqrt{a^2 + b^2}. This formula is derived from the Pythagorean theorem in geometry.

  4. Calculate the magnitude: Simply substitute the x and y components into the formula |\vec{v}| = \sqrt{a^2 + b^2} and solve for the magnitude.

  5. Find the direction (optional): If required, you can also find the direction of the vector using trigonometry. The angle of the vector from the positive x-axis can be found using \theta = \arctan{\frac{b}{a}}.

By following these steps, you can effectively find the magnitude of a vector given its components.