In the figure of Ex 1 if p is (2,4,5) find the co- ordinates of E

Answer

To find the coordinates of point E given that point P has coordinates (2, 4, 5) and point E lies in the YZ plane, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Coordinates of Point P:**
- The coordinates of point P are given as \( P(2, 4, 5) \).
- Here, \( x = 2 \), \( y = 4 \), and \( z = 5 \).

2. **Understand the Position of Point E:**
- Point E lies in the YZ plane.
- In the YZ plane, the x-coordinate is always 0 because any point in this plane has no displacement along the x-axis.

3. **Determine the x-coordinate of Point E:**
- Since point E is in the YZ plane, we set the x-coordinate of point E to 0.
- Thus, \( E(x, y, z) \) will have \( x = 0 \).

4. **Find the y-coordinate of Point E:**
- The y-coordinate of point E will be the same as the y-coordinate of point P since both points are at the same distance from the origin along the y-axis.
- Therefore, \( y = 4 \).

5. **Find the z-coordinate of Point E:**
- Similarly, the z-coordinate of point E will also be the same as the z-coordinate of point P.
- Thus, \( z = 5 \).

6. **Combine the Coordinates:**
- Now we can combine the coordinates we have found.
- The coordinates of point E are \( E(0, 4, 5) \).

### Final Answer:
The coordinates of point E are \( (0, 4, 5) \).