JEE Main2005MathematicsVector AlgebraActual

Let a = i - k , b =x i + j +(1-x) k and c =y i +x j +(1+x-y) k . Then [ a , b , c ] depends on

Options

Aonly y
Bonly x
Cboth x and y
Dneither x nor y

Correct answer

D. neither x nor y

Step-by-step solution

a = i - k , b =x i + j +(1-x) k and c =y i +x j +(1+x-y) k [ a b c ]= a ( b c ) aligned & b c = | array ccc i & j & k x & 1 & 1-x y & x & 1+x-y array |= i (1+x-x-x^2 )- j (x+x^2-x y-y+x y )+ k (x^2-y ) & a .( b c )=1 aligned which does not depend on x and y

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