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