# 10.8.4. Applications of Vectors

Find the resultant force acting on a book, which rests on a horizontal plane, when you try to move it by force of magnitude N parallel to the horizontal plane. The magnitude of the friction force between the book and the plane is N, consider that is the unit vector in the direction of the book's motion.

• AN
• BN
• CN
• DN

### Example

Find the resultant force acting on a book, which rests on a horizontal plane, when you try to move it by force of magnitude N parallel to the horizontal plane. The magnitude of the friction force between the book and the plane is N, consider that is the unit vector in the direction of the book's motion.

### Solution

Since is the unit vector in the direction of the movement of the book, represent the force with which the body moves as , and the friction force, which is in the opposite direction, as . The sum of the forces acting on an object is the resultant force, or , on the object. Find as follows:

The resultant force acting on the book is , so the magnitude of the resultant force is .

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