Write the value of k for which the planes x – 2y + kz = 4 and 2x + 5y – z = 9 are perpendicular.

Equation of the first plane is given as,

x–2y + kz=4 …………… (1)

and the equation of the second plane is given as,

2x + 5y–z=9 ……………… (2)

So, the normal vector of plane (1) is given by,

Similarly, the normal vector of plane (2) is given by,

When the two planes are perpendicular to each other, we should have,

2 - 10 - k=0

k= - 8.

Hence, the planes x–2y + kz=4 and 2x + 5y–z=9 will be perpendicular to each other if k= - 8.