For what value of a the vectors `2 hat i-3 hat j+4 hat k\ a n d\ a hat i+6 hat j-8 hat k` are collinear?

Explanation

To determine the value of \( a \) for which the vectors \( \mathbf{x} = 2\hat{i} - 3\hat{j} + 4\hat{k} \) and \( \mathbf{y} = a\hat{i} + 6\hat{j} - 8\hat{k} \) are collinear, we can use the property that two vectors are collinear if one is a scalar multiple of the other.

### Step-by-Step Solution:

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