1. The problem asks to find an example of a mechanical mechanism involving vector and scalar quantities with calculations. 2. In mechanical engineering, a common example is the calculation of the resultant force (a vector) and work done (a scalar). 3. Consider a force vector $\vec{F} = 5\hat{i} + 3\hat{j}$ Newtons acting on a point moving a displacement vector $\vec{d} = 4\hat{i} + 2\hat{j}$ meters. 4. The resultant force magnitude (scalar) is calculated by the formula: $$|\vec{F}| = \sqrt{F_x^2 + F_y^2}$$ where $F_x=5$ and $F_y=3$. 5. Calculate: $$|\vec{F}| = \sqrt{5^2 + 3^2} = \sqrt{25 + 9} = \sqrt{34} \approx 5.83$$ Newtons. 6. The work done (scalar) by the force along the displacement is given by the dot product: $$W = \vec{F} \cdot \vec{d} = F_x d_x + F_y d_y$$ 7. Calculate: $$W = 5 \times 4 + 3 \times 2 = 20 + 6 = 26$$ Joules. 8. Thus, the force vector has magnitude approximately 5.83 N, and the scalar work done is 26 J. This example shows vector quantities (force and displacement vectors) and scalar quantities (magnitude of force and work). Slug: "mechanical vectors" Subject: "mechanical engineering" Desmos: {"latex":"y=0","features":{"intercepts":true,"extrema":true}} q_count: 2