Mathematics

Problem

A force vector has components

F_x = -6\,\text{N}

and

F_y = 8\,\text{N}

. Determine: (i) the magnitude of the force, and (ii) the direction of the force measured anticlockwise from the positive

x

-axis, clearly stating the quadrant in which the vector lies.

Intuitive explanation

The key is recognizing that a force vector's magnitude and direction are two independent properties you can extract using the Pythagorean theorem and inverse trigonometry. Since $F_x$ is negative and $F_y$ is positive, the vector points into the second quadrant—so you'll need to adjust your angle calculation to reflect the true direction, not just the raw arctangent result.

Intuitive explanation

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