Given the line $L:\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-3}{-1}$ and the plane $II:x- 2y - z = 0 $

Of the assertions , the only one that is always true is,

L lies in II

We know that a line lies in a plane if every point on the line is a point on the plane. The coordinates of any point on line L are

$(3λ +1, 2λ - 1, -λ+3)$

Clearly, 3λ + 1- 4λ + 2 + λ - 3 = 0  i.e., the point (3λ + 1, 2λ - 1, -λ + 3) lies on the plane II.

Hence, the line L in the plane II.