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AP EAMCET2010MathematicsThree Dimensional Geometry

Let a = i -2 j +3 k , b =2 i +3 j - k and c = i + j +(2 -1) k . If c is parallel to the plane containing a , b , then is equal to

Options

  1. A0
  2. B1
  3. C-1
  4. D2

Correct answer

A. 0

Step-by-step solution

Given that, a = i -2 j +3 k b =2 i +3 j - k and c = i + j +(2 -1) k Also, since a and b lies in the same plane, then ( a b ) is perpendicular vector to this plane. Given that vector c is parallel to the plane containing a and b , so vector ( a b ) also perpendicular to the vector c ie, ( =90^ ) So, ( a b ) c should be equal to zero or ( a b ) c =0 ...(i) a b = | array ccc i & j & k 1 & -2 & 3 2 & 3 & -1 array |=(2-9) i +(6+1) j +(3+4) k =-7 i +7 j +7 k Then from Eq. (i) (-7 i +7 j +7 k ) ( i + j +(2 -1) k )=0 -7 +7

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