Given

For a,b Z and |a-b| 10. let the angle between the plane P : ax+y-z = b and the line L : x-1 = a - y = z + 1 be

Now rewriting the equation of line we get.

Now let,

Now we know that.

Angle between plane and line is given by,

3(a 2 + 4-4a)=8(a 2 +2)

5a 2 + 12a + 4 = 0

So a = , a = -2

Hence a = -2

So. the equation of plane will be.

P: -2x+y-z-b = 0

Now given, distance of point (6, -6,4) from plane is=

So, b = -4

Hence, a 4 + b 2 = 16 + 16 = 32

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