The vector in the direction of the vector $2\hat i-\hat j-2\hat k$ that has magnitude 9 units is:

$(6\hat i-\hat 3j-6\hat k)$

The correct answer is Option (4) → $(6\hat i-\hat 3j-6\hat k)$

Given vector: $\vec{v} = 2\hat{i} - \hat{j} - 2\hat{k}$

Magnitude of $\vec{v}$: $\sqrt{2^2 + (-1)^2 + (-2)^2} = \sqrt{4 + 1 + 4} = \sqrt{9} = 3$

Unit vector in the direction of $\vec{v}$: $\frac{1}{3}(2\hat{i} - \hat{j} - 2\hat{k})$

Vector with magnitude 9 in this direction: $9 \cdot \frac{1}{3}(2\hat{i} - \hat{j} - 2\hat{k}) = 3(2\hat{i} - \hat{j} - 2\hat{k}) = 6\hat{i} - 3\hat{j} - 6\hat{k}$