Maths-
General
Easy

Question

Let stack r with rightwards arrow on top equals left parenthesis stack a with rightwards arrow on top cross times stack b with rightwards arrow on top right parenthesis s i n invisible function application x plus left parenthesis stack b with rightwards arrow on top cross times stack c with rightwards arrow on top right parenthesis c o s invisible function application y plus 2 left parenthesis stack c with rightwards arrow on top cross times stack a with rightwards arrow on top right parenthesis where stack a with rightwards arrow on top stack c with rightwards arrow on top are three noncoplanar vectors. If stack r with rightwards arrow on top is perpendicular to stack a with rightwards arrow on top plus stack b with rightwards arrow on top plus stack v with rightwards arrow on top, then minimum value of x squared plus y squared

  1. pi to the power of 2 end exponent    
  2. fraction numerator pi to the power of 2 end exponent over denominator 4 end fraction    
  3. fraction numerator 5 pi to the power of 2 end exponent over denominator 4 end fraction    
  4. none of these    

The correct answer is: fraction numerator 5 pi to the power of 2 end exponent over denominator 4 end fraction

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Let a with ‾ on top equals i with ˆ on top plus j with ˆ on top plus k with rightwards arrow on top times b with rightwards arrow on top equals left square bracket x right square bracket i with ˆ on top plus left curly bracket s i n invisible function application left parenthesis x right parenthesis right curly bracket j comma c equals c subscript 1 i with ˆ on top plus c subscript 2 j with ˆ on top plus c subscript 3 k with ˆ on top be three non zero vectors,
such that vertical line stack c with rightwards arrow on top vertical line equals 1 angle between stack a with ‾ on top and stack b with ‾ on top is fraction numerator pi over denominator 4 end fraction, stack c with rightwards arrow on top is perpendicular to both stack a with rightwards arrow on top and stack b with ‾ on top. (where left square bracket x right square bracket equals Greatest integer function and left curly bracket x right curly bracket equals Fractional part of x right parenthesis. If f left parenthesis x right parenthesis equals left parenthesis stack a with rightwards arrow on top left parenthesis stack b with ‾ on top cross times stack c with ‾ on top right parenthesis right parenthesis to the power of 2 end exponent, then which of the following is correct for f left parenthesis x right parenthesis

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