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Let a=x^i+x2^j+2^k,b=3^i+^j+^k,c=(3x+11)^i+(x9)^j3^k be three vectors such that the angle  between a and b is acute and between c and a is obtuse, then x lies between
  1. (,1)(2,3)
     
  2. None of these
  3. (4, 5)
  4. (,0)
     


Solution

The correct option is A (,1)(2,3)
 
Since, angle between a and b is acute.
3x+x2+2>0 ie, x(,1)(2,)
Since, the angle between a and c is obtuse.
3x2+11x+x39x26<0
ie, x36x2+11x6<0
ie, (x1)(x2)(X3)<0
x(,1)(2,3)
 

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