99 Percentile Qs Bank for JEE MainMathematicsVector Algebra

If i +2 j +3 k , 3 i +2 j + k are sides of a parallelogram, then a unit vector is parallel to one of the diagonals of the parallelogram is

Options

Ai + j + k 3
Bi - j + k 3
Ci + j - k 3
D- i + j + k 3

Correct answer

A. i + j + k 3

Step-by-step solution

Let the position vector O A = i +2 j +2 k , O B =3 i +2 j + k Diagonal vector aligned & r O C = O A + A C & = O A + O B [ O B | A C ] & = i +2 j +2 k +3 i +2 j + k & =4( i + j + k ) aligned Unit vector of a diagonal = 4( i + j + k ) 4^2+4^2+4^2 = ( i + j + k ) 3

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