# 10.8.4. Applications of Vectors

A force of magnitude N is acting in the east direction on a cube, and each N can be represented by a directed line segment having a length cm. If an additional force of magnitude N was added to the previous force acting in the same direction, determine the magnitude of the force acting on the cube and the length of the directed line segment that represents this force.

• AN, cm
• BN, cm
• CN, cm
• DN, cm

### Example

A force of magnitude N is acting in the east direction on a cube, and each N can be represented by a directed line segment having a length cm. If an additional force of magnitude N was added to the previous force acting in the same direction, determine the magnitude of the force acting on the cube and the length of the directed line segment that represents this force.

### Solution

Let be the unit vector in the direction of the movement of the cube. Now represent the force acting on the cube as and the additional force 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 cube is , so the magnitude of the resultant force is . Given that each is represented by a directed line segment having a length of cm, find the length, , of the directed line segment that represents this force.

Thus, the length of the directed line segment that represents this force is .

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