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AP EAMCET202120 Aug 2021Evening ShiftMathematicsThree Dimensional GeometryActual

The equation of the plane passing through 3 i ^ + 2 j ^ + 6 k ^ and parallel to the vectors 2 i ^ + j ^ + k ^ and i - j + k is

Options

  1. Ax + y + z = 11
  2. B2   x - y - 3   z = - 14
  3. C2   x - y + z = 10
  4. Dx - 2   y + 3   z = 17

Correct answer

B. 2   x - y - 3   z = - 14

Step-by-step solution

Given that, the plane is parallel to the vectors 2   i ^ +   j ^ + k ^ and i ^ -   j ^ + k ^ So, N → = ( 2   i + j + k ) × ( i - j + k ) N → = i ^   j ^ i ^ 2 1 1 1 - 1 1 = 2 i ^ -   j ^ - 3 k ^ a → = 3 i ^ + 2   j ^ + 6 k ^ Equation of the plane is, ( r → - a → ) . N → = 0 ⇒ ( ( x - 3 ) i ^ + ( y - 2 )   j ^ + ( z - 6 ) k ^ ) . ( 2 i ^ -   j ^ - 3 k ^ ) = 0 ⇒ 2 ( x - 3 ) - ( y - 2 ) - 3 ( z - 6 ) = 0 ⇒ 2 x - y -

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