JEE Main201911 Jan 2019Evening ShiftMathematicsThree Dimensional GeometryActual

If the point (2, , ) lies on the plane which passes through the points (3,4,2) and (7,0,6) and is perpendicular to the plane 2 x-5 y=15, then 2 -3 is equal to :

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Correct answer

B. 7

Step-by-step solution

Let the normal to the required plane is n , then n = | array ccc i & j & k 4 & -4 & 4 2 & -5 & 0 array |=20 i +8 j -12 Equation of the plane (x-3) 20+(y-4) 8+(z-2) (-12)=05 x-15+2 y-8-3 z+6=05 x+2 y-3 z-17=0 (1) Since, equation of plane (1) passes through (2, , ) , then 10+2 -3 -17=0 2 -3 =7

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