for what value of k will the set of planes intersect in a line?x+2y-z=0x+9y-5z=0Kx-y+z=0

Plane through line of intersection of the two given planes is

S1 + nS2 = 0

Therefore x+2y-z + n( x+9y-5z) = 0

So x(1+n) + y(2+9n) +z( -1-5n) = 0

now compare coefficients

K = 1+n

2+9n= -1

-1-5n=1

Since n obtained is different for the two equations , for no value of k the three planes can intersect in a line

for three planes to intersect in a line

det=0.

therefoe, k=13/19.....i guess.

the answer is k=3/2