Answer:
1. To find the scalar product of force and displacement, you multiply the magnitude of the force by the magnitude of the displacement and then multiply by the cosine of the angle between them. So, the scalar product would be: \( F \cdot d = |F| \cdot |d| \cdot \cos(\theta) \), where \( |F| \) is the magnitude of the force, \( |d| \) is the magnitude of the displacement, and \( \theta \) is the angle between them.
2. To find the angle between the force and displacement vectors, you can use the dot product formula and rearrange it to solve for the angle: \( \cos(\theta) = \frac{F \cdot d}{|F| \cdot |d|} \). Once you have the angle, you can calculate its value.
3. The projection of the force vector onto the displacement vector can be found using the formula for the scalar projection: \( \text{Projection of } F \text{ onto } d = |F| \cdot \cos(\theta) \), where \( \theta \) is the angle between the force and displacement vectors.
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