Show that the vectors `2 hat i-3 hat j+4 hat k`and `-4 hat i+6 hat j-8 hat k`are collinear.

Explanation

To show that the vectors \( \mathbf{A} = 2\hat{i} - 3\hat{j} + 4\hat{k} \) and \( \mathbf{B} = -4\hat{i} + 6\hat{j} - 8\hat{k} \) are collinear, we can use the concept that two vectors are collinear if one is a scalar multiple of the other.

### Step-by-Step Solution:

1. **Identify the Vectors**:
\[ \mathbf{A} = 2\hat{i} - 3\hat{j} + 4\hat{k} \]
...