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Question: Answered & Verified by Expert
If a=i^+tanθj^+3sinθ2k^ and b=tanθj^-i^-2sinθ2k^ are orthogonal vectors and c=sin2θi^-2j^+2k^ makes an obtuse angle with X-axis, then θ=
MathematicsVector AlgebraTS EAMCETTS EAMCET 2020 (09 Sep Shift 1)
Options:
  • A (2n+1)π+tan-12, nZ
  • B nπ-tan-12, nZ
  • C (2n+1)π-tan-13, nZ
  • D (2n+1)π+tan-13, nZ
Solution:
1146 Upvotes Verified Answer
The correct answer is: nπ-tan-12, nZ

a·b=0

 -tanθ+tan2θ-6=0

tanθ=3, -2  ...i

Also a·c>0

sin2θ>0  ...ii

From (i) & (ii) tanθ=-2

θ=nπ-tan-12, nZ

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