AP EAMCET202317 May 2023Morning ShiftMathematicsVector AlgebraActual

Let b =3 i -2 j + k and c = i - j - k be two vectors. If a is a vector such that a + b + c = 0 , then | a b + b c + c a |=

Options

A15
B261
C234
D33

Correct answer

C. 234

Step-by-step solution

aligned & a + b + c =0 a =-( b + c ) & Now, a b + b c + c a =-( b + c ) b + b c - c ( b + c ) & =-( b b + c b )+ b c - c b - c c =3( b c ) aligned aligned & Now, ( b c )=(3 i -2 j + k ) ( i - j - k )=3 i +4 j - k & a b + b c + c a =3(3 i +4 j - k )=9 i +12 j -3 k & | a b + b c + c a |= 81+144+9 = 234 aligned

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