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JEE Advanced2010MathematicsVector AlgebraActual

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

A B =2 i +10 j +11 k A D =- i +2 j +2 k Angle ' ' between A B and A D is aligned & ( )= | array l A B A D A B | A D | array | & = | -2+20+22 (15)(3) |= 8 9 & ( )= 17 9 & Since, + =90^ & ( )= (90^ - ) & = ( )= 17 9 & aligned

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