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MHT CET202611 April 2026Evening ShiftMathematicsThree Dimensional GeometryActual

The vector equation of the plane passing through the point A(-2, 7, 5) and parallel to the vectors 4 i - j + 3 k and i + j + k is ...

Options

  1. Ar (-2 i + 7 j + 5 k ) = 26
  2. Br (4 i - j + 3 k ) = 27
  3. Cr (4 i - j + 5 k ) = 26
  4. Dr (-4 i - j + 5 k ) = 26

Correct answer

D. r (-4 i - j + 5 k ) = 26

Step-by-step solution

The normal vector n to the plane is perpendicular to both the given vectors. Thus, it is given by their cross product: n = (4 i - j + 3 k ) ( i + j + k ) n = vmatrix i & j & k 4 & -1 & 3 1 & 1 & 1 vmatrix n = i (-1 - 3) - j (4 - 3) + k (4 + 1) n = -4 i - j + 5 k The plane passes through the point A(-2, 7, 5) , so its position vector is a = -2 i + 7 j + 5 k . The vector equation of the plane is given by r n = a n . Calculating a n : a n = (-2 i + 7 j + 5 k ) (-4 i - j + 5 k ) a n = (-2)(-4) + (7)(-1) + (5)(5) a n =

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