AP EAMCET202317 May 2023Evening ShiftMathematicsVector AlgebraActual

For a positive real number , if the vector a = i -5 j +6 k satisfies the equation [ i ( a i )+ j ( a j )+ k ( a k )]^2=440 , then =

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Correct answer

C. 7

Step-by-step solution

[ i ( a i )+ j ( a j )+ k ( a k )]^2=440 aligned & [( i i ) a -( i a ) i +( j j ) a -( j a ) j +( k k ) a -( k a ) k ]^2=440 & [1 a - i +1 a -(-5) j +1 a -(6) k ]=440 & [3 a - a ]^2=440 4[ a ]^2=440 | a |^2=110 & ^2+25+36=110 =7 aligned

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