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JEE Advanced2010MathematicsThree Dimensional GeometryActual

If the distance between the plane A x-2 y+z=d and the plane containing the lines x-1 2 = y-2 3 = z-3 4 and x-2 3 = y-3 4 = z-4 5 is 6 , then |d| is

Correct answer

6

Step-by-step solution

Equation of plane containing the given lines is | array ccc x-1 & y-2 & z-3 2 & 3 & 4 3 & 4 & 5 array |=0 array rr & (x-1)(-1)-(y-2)(-2) & +(z-3)(-1)=0 & -x+1+2 y-4-z+3=0 & -x+2 y-z=0 (i) array Given plane is x-2 y+z=d Eqs. (i) and (ii) are parallel. Clearly, A=1 Now, distance between plane aligned & = | d 1+4+1 |= 6 & |d|=6 & aligned

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