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IIT JEE SOLVED PAPERS ON CO-ORDINATE GEOMETRY(3D)

Here is some solved problems from IIT-JEE Previous Year Papers.

Q. [IIT-JEE 2006] A plane passes through (1,-2,1) and is perpendicular to two planes 2x – 2y + z = 0 and x – y + 2z = 4, then the distance of the plane from the point (1,2,2) is
(a) 0     (b) 1     (c) √2      (d) 2√2
Solution :(d) Let equation of the plane through (1,-2,1) be            a(x-1) + b(y+2) + c(z-1)=0 ----------------(1)
Since plane (1) is perpendicular to 2x – 2y + z =0 & x – y +2z =4.
2a – 2b + c =0&a – b+2c=0
Solving we have a=k, b=k, c=0.
Substituting in (1), we have x + y + 1=0-----------(2)
Let p be perpendicular distance of the plane (2) from the point (1,2,2). Then   p = (1+2+3)/√(12+12)=2√2.
Q. [IIT-JEE 2003] The value of k (x-4)/1 = (y-2)/1 = (z-k)/2 lies in the plane 2x - 4y + z = 7, is
(a) 7      (b) -7      (c) no real value      (d) 4
Solution : (a) The given line passes through the point P(4,2,k) & lies in plane  2x - 4y + z = 7 . So, P must lie on the plane.
8 – 8 + k = 7     k=7.