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 find the value of \( \lambda \) such that 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 use the condition for parallel vectors.

### Step 1: Set up the condition for parallel vectors
Two vectors \( \mathbf{A} \) and \( \mathbf{B} \) are parallel if the ratios of their corresponding components are equal. This means:
\[ \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} \]
where \( \mathbf{A} = a_1\hat{i} + b_1\hat{j} + c_1\hat{k} \) and \( \mathbf{B} = a_2\hat{i} + b_2\hat{j} + c_2\hat{k} \).
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