JEE Main201911 Jan 2019Morning ShiftMathematicsVector AlgebraActual

Let a = i +2 j +4 k , b = i + j +4 k and c =2 i +4 j + ( ²-1 ) k be coplanar vectors. Then the non-zero vector a c is:

Options

A-10 i -5 j
B-14 i -5 j
C-14 i +5 j
D-10 i +5 j

Correct answer

D. -10 i +5 j

Step-by-step solution

a , b and c are coplanar | array ccc 1 & 2 & 4 1 & & 4 2 & 4 & ( ²-1 ) array |=0 ³- -16+2 (8- ²+1 )+4(4-2 )=0 ³-2 ²-9 +18=0 i.e. ( -2)( -3)( +3)=0 For =2, c =2 i +4 j +3 k a c = | array ccc i & j & k 1 & 2 & 4 2 & 4 & 3 array |=-10 i +5 j For =3 or -3, c =2 a a c =0 (Rejected)

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