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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

Let the equations of the sides P Q , Q R , R S and S P of a quadrilateral P Q R S are x + 2 y - 3 = 0 , x - 1 = 0 , x - 3 y - 4 = 0 and 5 x + y + 12 = 0 respectively. If θ is the angle between the diagonals P R and Q S , then the value of tan ⁡ θ is equal to

Options

  1. A2
  2. B- 2
  3. C1
  4. DNot defined

Correct answer

D. Not defined

Step-by-step solution

Solving x + 2 y - 3 = 0 and 5 x + 2 y + 12 = 0 , we get, P = - 3,3 Solving x + 2 y - 3 = 0 and x - 1 = 0 , we get, Q = 1,1 Solving x - 1 = 0 and x - 3 y - 4 = 0 , we get, R = 1 , - 1 Solving x - 3 y - 4 = 0 and 5 x + y + 12 = 0 , we get, S = - 2 , - 2 m 1 = s l o p e   o f     P R = - 1 ,   m 2 = s l o p e     o f     Q S = 1 ⇒ m 1 m 2 = - 1 ⇒ the angle between diagonals P R & Q S is 90 o Hence, tan 90 ° is not defined

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