A metal bar is in the xy-plane with one end of the bar at the origin. A force F = 97.00 N)i + (-3.00 N)j is applied to the bar at the point x = 3.00 m, y = 4.00 m. (a) In terms of unit vectors i and j, what is the position vector r for the point where the force is applied?

Verified step by step guidance

1. Identify the coordinates where the force is applied. In this problem, the force is applied at the point (x = 3.00 m, y = 4.00 m).
2. Recall the definition of a position vector. The position vector \( \vec{r} \) points from the origin to a specific point in space.
3. Write the position vector \( \vec{r} \) using the coordinates of the point. Since the point is at (3.00 m, 4.00 m), the position vector is \( \vec{r} = 3.00 \, \text{m} \, \hat{i} + 4.00 \, \text{m} \, \hat{j} \).
4. Express the position vector in terms of unit vectors i and j. The unit vector \( \hat{i} \) corresponds to the x-direction and \( \hat{j} \) corresponds to the y-direction.
5. Combine the components and unit vectors to form the complete position vector: \( \vec{r} = 3.00 \, \text{m} \, \hat{i} + 4.00 \, \text{m} \, \hat{j} \).

Key Concepts

Position Vector

A position vector represents the location of a point in space relative to a reference point, typically the origin. In a two-dimensional Cartesian coordinate system, it is expressed in terms of unit vectors i and j, where 'i' denotes the x-direction and 'j' denotes the y-direction. For a point (x, y), the position vector is given by r = xi + yj.

Unit Vectors

Unit vectors are vectors with a magnitude of one that indicate direction. In the Cartesian coordinate system, the unit vector 'i' points in the positive x-direction, while 'j' points in the positive y-direction. They are essential for expressing vectors in a clear and standardized form, allowing for easy manipulation and understanding of vector quantities.

Force Vector

A force vector is a representation of a force acting on an object, characterized by both magnitude and direction. It is typically expressed in terms of its components along the coordinate axes, such as F = Fxi + Fyj, where Fx and Fy are the force components in the x and y directions, respectively. Understanding force vectors is crucial for analyzing the effects of forces on objects in physics.