Find `lambda` and `mu` if `(2 hat i+6 hat j+27 hat k)xx( hat i+lambda hat j+mu hat k)= hat0dot`

Explanation

To solve the problem, we need to find the values of `lambda` and `mu` such that the cross product of the vectors \( \mathbf{A} = (2 \hat{i} + 6 \hat{j} + 27 \hat{k}) \) and \( \mathbf{B} = (\hat{i} + \lambda \hat{j} + \mu \hat{k}) \) equals the zero vector.

### Step-by-Step Solution:

1. **Set Up the Cross Product**:
We start by writing the cross product \( \mathbf{A} \times \mathbf{B} \) in determinant form:
\[
\mathbf{A} \times \mathbf{B} = \begin{vmatrix}
...