Orthogonality is a core linear-algebra concept used in ML to detect independence, remove redundancy, and measure similarity. In this task, you’ll implement a simple orthogonality checker for two vectors using the dot product.

$$
x \perp y \;\;\Longleftrightarrow\;\; x^\top y = \sum_{i=1}^{n} x_i y_i = 0
$$

## Requirements

Implement the function:
```python
import numpy as np

def is_orthogonal(x, y, tol=1e-9):
    \"""
    Checks whether two vectors are orthogonal (perpendicular) using the dot product.

    Args:
        x (np.ndarray): First vector of length n.
        y (np.ndarray): Second vector of length n.
        tol (float): Non-negative tolerance. Treat vectors as orthogonal if |dot(x, y)| <= tol.

    Returns:
        bool: True if x and y are orthogonal within tolerance, otherwise False.
    \"""
    # Your solution below
```

**Rules:**
- Compute the dot product manually or via NumPy basic ops (no prebuilt distance/similarity helpers).
- Use `tol` to handle floating-point error: return `True` if `abs(dot) <= tol`.
- Return a single boolean value.
- Keep it as a single Python function using only NumPy + built-in libraries.
- Don’t print; just return.

## Example

```python
x = np.array([1.0, 2.0, -1.0])
y = np.array([2.0, -1.0, 0.0])

is_orthogonal(x, y)
```

Output:
```python
True
```

Retrieval Precision At K

Maximum Average Subarray I

Orthogonality

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1065. Orthogonality

Examples

Constraints

Similar Questions

Argument	Type
x	np.ndarray
y	np.ndarray
tol	float