Find the value of λ so that the vector `vecA=2hati+lambda hatj+hatk and vecB=4hati-2hatj+2hatk` are perpendicular to each other.

Explanation

To find the value of λ such that the vectors \(\vec{A} = 2\hat{i} + \lambda \hat{j} + \hat{k}\) and \(\vec{B} = 4\hat{i} - 2\hat{j} + 2\hat{k}\) are perpendicular, we can use the property of the dot product. Two vectors are perpendicular if their dot product is zero.

### Step-by-step Solution:

1. **Write the Dot Product Formula**:
The dot product of two vectors \(\vec{A}\) and \(\vec{B}\) is given by:
\[
\vec{A} \cdot \vec{B} = A_x B_x + A_y B_y + A_z B_z
...