# Express the force as a cartesian vector. (figure 1) ## General guidance

Concepts and reason
Cartesian vector representation: Consider a vector A having components along x, y and z axes. Then the vector A can be written in Cartesian vector from as: Here, , and are the components of vector A along x, y and z axes and , and are the unit vectors along x, y and z axes. Cartesian vectors are used to simplify the vector algebra in three dimensions.

Fundamentals

The Cartesian form of the force F is, ……. (1) Here, the components of the force vector along x, y and z Fare , and respectively.

## Step-by-step

### Step 1 of 3

Draw the free body diagram of the system as shown below. After identifying the forces acting in the system, the free body diagram of the system is drawn as shown above.

### Step 2 of 3

Calculate the z component of the force using relation. Substitute, for in relation above and calculate . Calculate the y component of the force using relation. Substitute, for in relation above and calculate . Calculate horizontal component of the force on xy plane. Substitute, for in relation above and calculate . Calculate the x component of the force using relation. Substitute, for in relation above and calculate . The force along each coordinate axis are calculated as per the inclination made by the force F.

### Step 3 of 3

Calculate the Cartesian vector form of force. Using equation (1), Substitute for , for , for . The Cartesian vector form of force is .

The sum of the force components along each coordinate axis gives the Cartesian vector form of the given force.

The Cartesian vector form of force is .