A plumber steps out of his truck, walks `60m` east and `35m` south and then taken an elevator, `12m` down to the basement of a building where a bad leak is occurring. Assume x axis is east , y-exis is north and z-axis us up, Find displacement of plumber in term of conventional co-ordinate system ?

Explanation

To find the displacement of the plumber in terms of the conventional coordinate system, we can break down the problem step by step.

### Step 1: Define the Coordinate System
- The x-axis represents the east direction.
- The y-axis represents the north direction.
- The z-axis represents the vertical direction, where positive z is up and negative z is down.

### Step 2: Determine the Movements
1. The plumber walks **60 meters east**:
- In terms of coordinates, this is represented as \( +60 \hat{i} \).

2. Then, he walks **35 meters south**:
- South is in the negative y direction, so this is represented as \( -35 \hat{j} \).

3. Finally, he takes an elevator **12 meters down**:
- Down is in the negative z direction, so this is represented as \( -12 \hat{k} \).

### Step 3: Combine the Displacements
Now we can combine these movements into a single displacement vector \( \vec{D} \):
\[ \vec{D} = 60 \hat{i} - 35 \hat{j} - 12 \hat{k} \]

### Final Displacement Vector
Thus, the displacement of the plumber in terms of the conventional coordinate system is:
\[ \vec{D} = 60 \hat{i} - 35 \hat{j} - 12 \hat{k} \]

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