Given: Plane 2x – y + z = 0 is parallel to the line

To find: value of a

Formula Used: If two lines with direction ratios a₁:a₂:a₃ and b₁:b₂:b₃ are perpendicular, then

a₁b₁ + a₂b₂ + a₃b₃ = 0

Explanation:

Since the plane is parallel to the line, the normal to the plane will be perpendicular to the line.

Equation of the line can be rewritten as

Direction ratio of the normal to the plane is 2 : -1 : 1

Direction ratio of line is 1 : -2 : a

Therefore,

2 + 2 + a = 0

a = -4

Therefore, a = -4