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JEE Main20248 Apr 2024Morning ShiftMathematicsVector AlgebraActual

Let a =9 i -13 j +25 k , b =3 i +7 j -13 k and c =17 i -2 j + k be three given vectors. If r is a vector such that r a =( b + c ) a and r ( b - c )=0 , then |593 r +67 a |^2 (593)^2 is equal to___________

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aligned & a =9 i -13 j +25 k & b =3 i +7 j -13 k & c =17 i -2 j + k & b + c =20 i +5 j -12 k & b - c =-14 i +9 j -14 k & ( r -( b + c ))_ a =0 & r -( b + c )= a & r = a + b + c & But r ( b - c )=0 & ( a + b + c ) ( b - c )=0 & a b + b b + c b - a c - b c - c c =0 & = c c - b b a b - a c = 294-227 -389=204 = -67 593 & r = b + c - 67 593 a & 593 r +67 a =593( b + c ) & | b + c |^2=569 aligned

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