If vectors u = 2i − j − k and v = λi + j + 5k are perpendicular, what is the value of λ?

Let the first vector be $\vec{u}$ and the second vector be $\vec{v}$.

$$\vec{u} = 2\hat{i} - \hat{j} - \hat{k}$$ $$\vec{v} = \lambda\hat{i} + \hat{j} + 5\hat{k}$$

If two vectors are perpendicular, their dot product is zero.

$$\vec{u} \cdot \vec{v} = 0$$

$$(2)(\lambda) + (-1)(1) + (-1)(5) = 0$$ $$2\lambda - 1 - 5 = 0$$ $$2\lambda - 6 = 0$$

$$2\lambda = 6$$ $$\lambda = \frac{6}{2}$$ $$\lambda = 3$$

The calculated value $\lambda = 3$ matches option (a).

The final answer is $\text{(a)} 3$.