how is the displacement of bc obtained? explain about steps to get it please

give the calculation step by step as like as full answer in 2 steps and explanation block in every steps.
And final answe

Question

how is the displacement of bc obtained? explain about steps to get it please

give the calculation step by step as like as full answer in 2 steps and explanation block in every steps. 
And final answer summary
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VIPSolutions · Accepted Answer

Certainly! However, the question "how is the displacement of BC obtained?" seems to lack context. Typically, "displacement of BC" refers to the change in position from point B to point C in a physics or engineering problem—often a vector connecting two points or the result of a process (like a beam's deflection at point C due to a load at B).

**For a generic explanation**, here’s a step-by-step approach to calculating the displacement between two points B and C on a straight path (or coordinate system):

---

### **Definition of Parameters**
- **Displacement (sBC)**: The straight-line distance and direction from point B to point C.
- **Coordinates of B (xB, yB)**: The position of point B.
- **Coordinates of C (xC, yC)**: The position of point C.

---

## **Step 1: Identify the Coordinates of Points B and C**

**Explanation:**  
To calculate displacement, the positions of points B and C must be known. These are typically given as coordinates in 2D or 3D space.

**Example:**  
Suppose  
- B has coordinates (xB, yB)  
- C has coordinates (xC, yC)

---

## **Step 2: Calculate the Displacement Using the Distance Formula**

**Explanation:**  
The displacement from B to C is the straight-line distance between these points. In 2D, the displacement magnitude is given by the distance formula:

$$
s_{BC} = \sqrt{(x_C - x_B)^2 + (y_C - y_B)^2}
$$

- For 3D:  
$$
s_{BC} = \sqrt{(x_C - x_B)^2 + (y_C - y_B)^2 + (z_C - z_B)^2}
$$

**Example Calculation:**  
If B = (2, 3), C = (7, 11):

$$
s_{BC} = \sqrt{(7 - 2)^2 + (11 - 3)^2}
$$
$$
s_{BC} = \sqrt{5^2 + 8^2}
$$
$$
s_{BC} = \sqrt{25 + 64}
$$
$$
s_{BC} = \sqrt{89}
$$
$$
s_{BC} \approx 9.43
$$

---

### **Final Answer Summary**

The displacement from B to C is obtained by first identifying the coordinates of B and C, and then applying the distance formula. For the example above, the displacement sBC ≈ 9.43 units.

---

**Key Points:**
- Displacement is a vector; this calculation gives its magnitude.
- The direction can be found by the angle or by expressing the displacement as a vector:  
  $\vec{s}_{BC} = (x_C - x_B)\hat{i} + (y_C - y_B)\hat{j}$

---

**If the context is different (e.g., beam deflection, kinematics), please provide additional details for a tailored solution.**

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