Given:

1. Equation of line is

2. Equation of plane is 2x – 3y + kz = 0

Formula Used: If two direction ratios are perpendicular, then

a �₁a₂ + b₁b₂ + c₁c₂ = 0

Explanation:

Direction ratios of given line is (3, 4, 5)

Direction ratios of given plane is (2, -3, k)

Since the given line is parallel to the plane, the normal to the plane is perpendicular to the line.

So direction ratio of line is perpendicular to direction ratios of plane.

⇒ 3× 2 + 4× -3+ 5× k = 0

⇒ 6 – 12 + 5k = 0

Therefore,