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NDA2021MathematicsThree Dimensional GeometryActual

A B C D E F G H is a cuboid with base A B C D . Let A(0,0,0), B(12,0,0), C(12,6,0) and G(12,6,4) be the vertices. If is the angle between A B and A G ; is the angle between A C and A G , then what is the value of 2 + 2 ?

Options

  1. A40 49
  2. B64 49
  3. C120 49
  4. D160 49

Correct answer

B. 64 49

Step-by-step solution

Direction cosines of A B=1,0,0 . Direction cosines of AG = aligned & = 12 12^2+6^2+4^2 , 6 12^2+6^2+4^2 , 4 12^2+6^2+4^2 & = 6 7 , 3 7 , 2 7 aligned Direction cosines of AC aligned & = 12 12^2+6^2 , 6 12^2+6^2 , 0 & 2 5 , 1 5 , 0 aligned aligned & = 6 7 +0+0= 6 7 & = 6 7 2 5 + 3 7 1 5 + 2 7 0= 15 7 5 aligned Now, 2 + 2 =2 [ ^2 + ^2 ]-2=2 [ 36 49 + 225 49 5 ]-2= 64 49

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