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MHT CET202312 May 2023Morning ShiftMathematicsVector AlgebraActual

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

Options

  1. A8 9
  2. B17 9
  3. C1 9
  4. D4 5 9

Correct answer

B. 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 aligned & ( + )= (90^ ) & - =0 & 8 = 17 & 64 ^2 =17 (1- ^2 ) & 81 ^2 =17 & = 17 9 aligned

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