MHT CET202019 Oct 2020Morning ShiftMathematicsVector AlgebraActual

If a, b, c are distinct positive numbers and vectors a +a +c k , + k and c +c +b k lie in a plane, then

Options

Ac is A.M. of a and b
Bc ²=0
Cc is H . M . of a and b
Dc is G.M. of a and b

Correct answer

D. c is G.M. of a and b

Step-by-step solution

(B) since, three vectors are coplanar | array lll a & a & c 1 & 0 & 1 c & c & b array |=0 Applying C ₁ C ₁- C ₂ | array lll 0 & a & c 1 & 0 & 1 0 & c & b array |=0 Expanding along C₁ , we get -1 (a b-c² )=0 a b=c² c is G.M. of a and b

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