Vectors Physics Example 1

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Example 1

easy

Find the magnitude and direction of the vector with components

v_x = 3

and

v_y = 4

Solution

1
Use the Pythagorean theorem for the magnitude of the vector.
2
Magnitude: $|\vec{v}| = \sqrt{v_x^2 + v_y^2} = \sqrt{9 + 16} = \sqrt{25} = 5$
3
Direction: $\theta = \tan^{-1}\left(\frac{v_y}{v_x}\right) = \tan^{-1}\left(\frac{4}{3}\right) \approx 53.1°$

Answer

|\vec{v}| = 5, \quad \theta \approx 53.1°

Any vector can be described by its magnitude and direction or by its components. The Pythagorean theorem gives the magnitude, and the inverse tangent gives the angle.

About Vectors

Mathematical quantities that possess both a magnitude (size) and a direction, represented graphically as arrows.

Learn more about Vectors →

More Vectors Examples

Example 2 medium

Add the vectors: [formula] at [formula] (east) and [formula] at [formula] (north). Find the resultan

Example 3 medium

A force of [formula] acts at [formula] above the horizontal. Find the horizontal and vertical compon

Example 4 medium

Two forces act on an object: [formula] east and [formula] north. Find the magnitude and direction of

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