The value of λ, for which the two vectors $2\hat i-\hat j + 2\hat k$ and $3\hat i +λ\hat j+\hat k$ are perpendicular, is:

8

The correct answer is Option (2) → 8

For perpendicular vectors, dot product = $0$.

$(2,-1,2)\cdot(3,\lambda,1)=0$

$2\cdot 3 + (-1)\cdot \lambda + 2\cdot 1 = 0$

$6 - \lambda + 2 = 0$

$8 - \lambda = 0$

$\lambda = 8$

The required value of $\lambda$ is 8.