Long description: Fig7P

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• The diagram shows a right-angled triangle representing a vector labeled with a magnitude of \(u\).
• The angle \(\theta\) is indicated between the horizontal side and the hypotenuse representing \(u\).
• The horizontal side (adjacent) of the triangle is labeled with the magnitude \(u \text{ cos } \theta\), corresponding to the \(\text{i}\) unit vector direction.
• The vertical side (opposite) of the triangle is labeled with the magnitude \(u \text{ sin } \theta\), corresponding to the \(\text{j}\) unit vector direction.
• The overall structure illustrates the decomposition of a vector \(u\) into its perpendicular components, \(u \text{ cos } \theta\) along the horizontal axis and \(u \text{ sin } \theta\) along the vertical axis.