MHT CET20249 May 2024Morning ShiftMathematicsVector AlgebraActual

If a = i + j + k , a b =1 and a b = j - k , then b is

Options

Ai - j + k
B2 j - k
Ci
D2 i

Correct answer

C. i

Step-by-step solution

Given, a = i + j + k and a b = j - k a ~b =1 Let b =x i +y j +z k aligned & a b = | array ccc i & j & k 1 & 1 & 1 x & y & z array | & j - k =( z -y) i - j ( z -x)+ k (y-x) & z -y=0 ...(i) & z -x=-1...(ii) aligned array ll & y-x=-1 ...(iii) & Also, a ~b =1 & x+y+ z =1 ...(iv) array Solving (i), (ii), (iii) and (iv), we get aligned & x=1, y=0, z =0 & ~b = i aligned

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