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AP EAMCET20227 Jul 2022Morning ShiftMathematicsThree Dimensional GeometryActual

Suppose (l₁, m₁, n₁ ) and (l₂, m₂, n₂ ) are the directional cosines of two lines and is the angle between them and = (l₁ l₂+m₁ m₂+n₁ n₂ ) . Let A=(1,-2,3) , B=(3,1,-3) and C=(-3,1,3) be the vertices of A B C . Then, A=

Options

  1. A- 1 35
  2. B1 7
  3. C- 1 7
  4. D1 35

Correct answer

D. 1 35

Step-by-step solution

Let DC's of A B and A C are l₁, m₁, n₁ and l₂, m₂, n₂ respectively. DR's of A B: 2,3,-6 DR ^ s of A C:-4,3,0 l₁= 2 7 , m₁= 3 7 , n₁= -6 7 and l₂=- 4 5 , m₂= 3 5 , n₂=0 A= (l₁ l₂+m₁ m₂+n₁ n₂ )= 2 7 ( -4 5 )+ 3 7 3 5 +0= 1 35

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