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 need to establish that one vector can be expressed as a scalar multiple of the other.

### Step-by-Step Solution:

1. **Define the Vectors**:
Let \( \mathbf{A} = 2 \hat{i} - 3 \hat{j} + 4 \hat{k} \) and \( \mathbf{B} = -4 \hat{i} + 6 \hat{j} - 8 \hat{k} \).

2. **Set Up the Collinearity Condition**:
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