Maths-
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Easy

Question

If stack a with minus on top equals left parenthesis 3 comma negative 15 right parenthesis comma stack b with minus on top equals left parenthesis 12 comma negative 3 right parenthesis are given vectors. A vector stack c with minus on top which is perpendicular to z-axis satisfying stack c with minus on top times stack a with minus on top equals 9 and stack c with minus on top times stack b with minus on top equals negative 4 then

  1. left parenthesis c with ‾ on top comma i with ‾ on top right parenthesis less than pi over 4    
  2. left parenthesis c with minus on top comma i with minus on top right parenthesis greater than pi over 2    
  3. left parenthesis c with ‾ on top comma j with ‾ on top right parenthesis greater than pi over 2    
  4. left parenthesis c with ‾ on top comma j with ‾ on top right parenthesis less than pi over 2    

The correct answer is: left parenthesis c with ‾ on top comma j with ‾ on top right parenthesis greater than pi over 2

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a with minus on top equals left parenthesis c o s invisible function application theta right parenthesis times i with minus on top minus left parenthesis s i n invisible function application theta right parenthesis j with minus on top comma b with minus on top equals left parenthesis s i n invisible function application theta right parenthesis times i with minus on top plus left parenthesis c o s invisible function application theta right parenthesis j with minus on top comma c with minus on top equals k with minus on top comma r with minus on top equals 17 i with minus on top plus 7 j with minus on top plus 15 k with minus on top and stack r with ‾ on top equals x stack a with ‾ on top plus y stack b with ‾ on top plus z stack c with ‾ on top. The range of x plus y plus z is

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a with rightwards arrow on top equals left parenthesis c o s invisible function application theta right parenthesis i with rightwards arrow on top minus left parenthesis s i n invisible function application theta right parenthesis j with rightwards arrow on top comma b with rightwards arrow on top equals left parenthesis s i n invisible function application theta right parenthesis i with rightwards arrow on top plus left parenthesis c o s invisible function application theta right parenthesis j with rightwards arrow on top comma c with rightwards arrow on top equals k with rightwards arrow on top comma r with rightwards arrow on top equals 7 i with rightwards arrow on top plus j with rightwards arrow on top plus 10 k with rightwards arrow on top if stack r with rightwards arrow on top equals x stack a with rightwards arrow on top plus y stack b with rightwards arrow on top plus z stack c with rightwards arrow on top, then

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