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99 Percentile Qs Bank for JEE MainMathematicsVector Algebra

Two adjacent of sides parallelogram ABCD are given by AB =2 i +10 j +11 k and AD =- i +2 j +2 k . The side AD is rotated by angle in plane of parallelogram so that AD becomes AD ^ . If AD ^ makes a right angle with the side A B , then the cosine of the angle is given by

Options

  1. A8 9
  2. B1 9
  3. C17 9
  4. D4 5 9

Correct answer

C. 17 9

Step-by-step solution

Let be the angle between AB and AD aligned & = AB AD | AB || AD | & = (2 i +10 j +11 k ) (- i +2 j +2 k ) 4+100+121 1+4+4 & = -2+20+22 225 9 & = 40 45 & = 8 9 & = 1- ( 8 9 )^2 = 17 9 aligned is the angle of rotation of A D The angle between side AB and AD aligned & = + & =90^ aligned array ll & ( + )= (90^ ) & - =0 & 8 = 17 & 64 ^2 =17 (1- ^2 ) & 81 ^2 =17 & = 17 9 array

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