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MHT CET2019Morning ShiftMathematicsVector AlgebraActual

The vector equation of the plane r = 2 i ^ + k ^ + λ i ^ + μ i ^ + 2 j ^ - 3 k ^ in scalar product from is r . 3 i ^ + 2 k ^ = α , then α = …

Options

  1. A2
  2. B3
  3. C1
  4. D0

Correct answer

A. 2

Step-by-step solution

Given, equation of plane r = 2 i ^ + k ^ + λ i ^ + μ i ^ + 2 j ^ - 3 k ^ … (i) H e r e , plane (i) passing through a (let) = 2 i ^ + k ^ and parallel to vector b (let) = i ^ and c = i ^ + 2 j ^ - 3 k ^ We know that equation of plane passing through a point a and parallel to non-parallel vectors b and c is r . b × c = a . b × c = a b c Now, a b c = 2 0 1 1 0 0 1 2 - 3 = 2 0 - 0 + 1 2 - 0 = 2 and b × c = i ^ j ^ k ^ 1 0 0 1 2 - 3 = 3 i ^ + 2 k ^ ∴ r 3 i ^ + 2 k ^ = 2 T h e r e f o r e , α = 2

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