If two vectors `2hat(i)+3hat(j)-hat(k)` and `-4hat(i)-6hat(j)-lambda hat(k)` are parallel to each other,then find the value of `lambda`

Explanation

To determine the value of \( \lambda \) for which the vectors \( \mathbf{A} = 2\hat{i} + 3\hat{j} - \hat{k} \) and \( \mathbf{B} = -4\hat{i} - 6\hat{j} - \lambda \hat{k} \) are parallel, we can follow these steps:

### Step 1: Understand the condition for parallel vectors
Two vectors are parallel if one is a scalar multiple of the other. This means we can express \( \mathbf{A} \) as \( n \mathbf{B} \) for some scalar \( n \).

### Step 2: Set up the equations based on the components
From the vectors, we can write:
\[
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