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Most Important Selected Qs for JEE AdvancedMathematicsThree Dimensional Geometry

Given f( a , b , c ) 2 , where f( a , b , c )= | a b - 1 2 |+(3 ~b -2 c )^2+ ⁻¹ (1+ (( a -1)^2+( b -2)^2 ) ) . Also denotes the plane through the line y b + z c =1, x=0 and parallel to the line x a - z c =1, y=0 . If the plane cuts the co-ordinate axes at A , B , C , then volume of tetrahedron OABC , O being the origin, is

Correct answer

1

Step-by-step solution

Clearly, a =1, ~b =2, c =3 . The second line can be written as x-a a = y 0 = z c ...(1) Now equation of plane through the line y ~b + z c =1, x =0 is ( y ~b + z c -1 )+ x =0 or x + y b + z c =1...(2) plane (2) is parallel to the line (1) a + 1 6 0+ 1 c c =0 =- 1 a equation of plane is - x a + y b + z c =1 or - x 1 + y 2 + z 3 =1 aligned & A (-1,0,0), B (0,2,0), C (0,0,3) & volume of tetrahedron aligned OABC = | 1 6 [ array lll - i & 2 j & 3 k array ] |=6 1 6 [ i j k ]=1

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