A mosquito net over a `7ftxx4ft` bed is 3 ft high. The net hs a hole at one corner of the bed through which diagonally opposite upper corner of the net. A. Find the magnitude of the displaceentof the mosquito. B. Taking the hole as the origin, the length of the bed as the X-axis, its width as teh Y-axis, and verticallup as the Z-axis, write the components of the displacement vector.

Explanation

To solve the problem step by step, we will break it down into two parts as mentioned in the question.

### Part A: Finding the Magnitude of the Displacement of the Mosquito

1. **Identify the Coordinates**:
- Let's consider the hole at the origin (0, 0, 0).
- The dimensions of the bed are 7 feet (length) and 4 feet (width), with a height of 3 feet.
- The diagonally opposite upper corner of the net will have coordinates (7, 4, 3).

2. **Calculate the Displacement Vector**:
- The displacement vector from the hole (origin) to the upper corner of the net can be represented as:
\[ \vec{d} = (7 - 0, 4 - 0, 3 - 0) = (7, 4, 3) \]

3. **Magnitude of the Displacement Vector**:
- The magnitude of the displacement vector \(\vec{d}\) can be calculated using the formula:
\[ |\vec{d}| = \sqrt{x^2 + y^2 + z^2} \]
- Substituting the values:
\[ |\vec{d}| = \sqrt{7^2 + 4^2 + 3^2} = \sqrt{49 + 16 + 9} = \sqrt{74} \]

4. **Final Result for Part A**:
- The magnitude of the displacement of the mosquito is:
\[ |\vec{d}| = \sqrt{74} \text{ feet} \]

### Part B: Components of the Displacement Vector

1. **Identify the Components**:
- The components of the displacement vector can be directly taken from the coordinates of the upper corner of the net:
- \(x\) component (length of the bed): 7 feet
- \(y\) component (width of the bed): 4 feet
- \(z\) component (height of the net): 3 feet

2. **Write the Components**:
- Therefore, the components of the displacement vector \(\vec{d}\) are:
\[ \vec{d} = (7, 4, 3) \]

### Final Answers:
- **Part A**: The magnitude of the displacement of the mosquito is \(\sqrt{74}\) feet.
- **Part B**: The components of the displacement vector are \( (7, 4, 3) \).