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JEE Main20246 Apr 2024Morning ShiftMathematicsVector AlgebraActual

Let a =2 i -3 j +4 k , b =3 i +4 j -5 k and a vector c be such that a ( b + c )+ b c = i +8 j +13 k . If a c =13 , then (24- b c ) is equal to_______

Correct answer

0

Step-by-step solution

aligned & a b + a c + b c =(1,8,13) & a ( a b )+ a ( a c )+ a ( b c ) & = a ( i +8 j +13 k ) aligned aligned & ( a b ) a -a^2 b +( a c ) a -a^2 c +( a c ) b -( a b ) c = a ( i +8 j +13 k ) & -26 a -29 b +13 a -29 c +13 b +26 c = a ( i +8 j +13 k ) aligned aligned & -13 a -16 b -3 c = a ( i +8 j +13 k ) & -13 a b -16 ~b ^2-3 b c = a ( i +8 j +13 k ) b & (-13)(-26)-16(50)-3 b c = | array ccc 2 & -3 & 4 1 & 8 & 13 3 & 4 & -5 array | & -462-3 b c =-396 & b c =-22 aligned Hence 24- b c =46

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