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99 Percentile Qs Bank for JEE MainMathematicsVector Algebra

If the angle between the vectors a =2 x^2 i +4 x j + k and b =7 i -2 j +x k is such that 90^ < < 180^ , then x lies in the interval

Options

  1. A(0, 1 2 )
  2. B( 1 2 , 1 )
  3. C(1, 3 2 )
  4. D( 1 2 , 3 2 )

Correct answer

A. (0, 1 2 )

Step-by-step solution

Given, a =2 x^2 i +4 x j + k b =7 i -2 j +x k , also 90^ < < 180^ We know that, = a b | a || b | = (2 x^2 i +4 x j + k ) (7 i -2 j +x k ) 4 x^4+16 x^2+1 49+4+x^2 = 14 x^2-8 x+x 4 x^4+16 x^2+1 53+x^2 = 14 x^2-7 x 4 x^4+16 x^2+1 53+x^2 = 7 x(2 x-1) 4 x^4+16 x^2+1 53+x^2 lies between (90^ , 180^ ) ie, is negative in Ind quadrant. So, RHS is also negative ie, 7 x(2 x-1) 4 x^4+16 x^2+1 53+x^2 < 07 x(2 x-1) < 0 So, x (0, 1 2 )

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