Let the distance between two parallel lines be 5 units and a point P lie between the lines at a unit distance from one of them. An equilateral triangle PQR is formed such that Q lies on one of the par

Question

Let the distance between two parallel lines be 5 units and a point P lie between the lines at a unit distance from one of them. An equilateral triangle PQR is formed such that Q lies on one of the parallel lines, while R lies on the other. Then ( QR ) 2 is equal to _______ -.

TestHub · Accepted Answer

PR = cosec θ , PQ = 4 sec ( 30 + θ ) For equilateral ​ d = PR = PQ ⇒ cos ( θ + 3 0 ∘ ) = 4 sin θ ⇒ 2 3 ​ ​ cos θ − 2 1 ​ sin θ = 4 sin θ ⇒ tan θ = 3 3 ​ 1 ​ QR 2 = d 2 = cosec 2 θ = 28 ​

Mathematics - Vector Question with Solution | TestHub

Doubts & Discussion