The Pythagorean theorem can be used because the perpendicular component displacements of a vector in an orthonormal Cartesian plane form the two legs of a right triangle, with the vector itself acting as the hypotenuse. The theorem relates the lengths of the legs to the length of the hypotenuse, allowing the calculation of the vector's magnitude (length).
Conditions: The coordinate axes are perpendicular (orthonormal).; The vector is drawn from the origin to its terminal point.; The magnitude is the Euclidean length of the vector.
The Pythagorean theorem can be used because the perpendicular component displacements of a vector in an orthonormal Cartesian plane form the two legs of a right triangle, with the vector itself acting as the hypotenuse. The theorem relates the lengths of the legs to the length of the hypotenuse, allowing the calculation of the vector's magnitude (length).
Conditions: The coordinate axes are perpendicular (orthonormal).; The vector is drawn from the origin to its terminal point.; The magnitude is the Euclidean length of the vector.