AP EAMCET202318 May 2023Morning ShiftMathematicsVector AlgebraActual

If a =2 i - j +3 k , b =-3 i +5 j -4 k and c =6 i -4 j +5 k , then ( a b ) ( b c )=

Options

A-216
B243
C81
D-27

Correct answer

A. -216

Step-by-step solution

a =2 i - j +3 k , b =-3 i +5 j -4 k , c =6 i -4 j +5 k a b | array ccc i & j & k 2 & -1 & 3 -3 & 5 & -9 array |= i (4-15)- j (-8+9)+ k (10-3)=-11 i - j +7 k b c | array ccc i & j & k -3 & 5 & -4 6 & -4 & 5 array |= i (25-16)- j (-15+24)+ k (12-30)=9 i -9 j -18 k aligned & ( a b ) ( b c )=(-11 i - j +7 k ) (9 i -9 j -18 k ) & =-99+9-126=-216 aligned

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