Find the value of k such that the line is perpendicular to the plane 3x – y – 2z = 7.

Question

Philoid · Accepted Answer

Here, given midline is perpendicular to plane 3x – y – 2z = 7.

We know that line is perpendicular to plane a₂x + b₂y + c₂z + d₂ = 0 if

So, normal vector of plane is parallel to line .

So, direction ratios of normal to plane are proportional to the direction ratios of line .

Here,

By cross multiplying the last two we have

– 2k = 4

⇒ k = – 2