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MHT CET202314 May 2023Evening ShiftMathematicsThree Dimensional GeometryActual

A vector parallel to the line of intersection of the planes r (3 i - j + k )=1 and r ( i +4 j -2 k )=2 is

Options

  1. A-2 i +7 j +13 k
  2. B2 i -7 j +13 k
  3. C- i +4 j +7 k
  4. Di -4 j +7 k

Correct answer

A. -2 i +7 j +13 k

Step-by-step solution

The line of intersection of the planes r (3 i - j + k )=1 and r ( i +4 j -2 k )=2 is perpendicular to each of the normal vectors n₁ =3 i - j + k and n₂ = i +4 j -2 k . The line is parallel to the vector n ₁ n ₂ aligned n ₁ n ₂ & = | array ccc i & j & k 3 & -1 & 1 1 & 4 & -2 array | & =-2 i +7 j +13 k aligned

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