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A line 2x + 3y – 1 = 0 intersects the three sides BC, CA, and AB of the triangle ABC in P, Q, R respectively. Then

If m₁, m₂ are the roots of the equation x² – ax – a – 1 = 0, then the area of the triangle formed by the three st. lines y = m₁x, y=m₂x and y = a(a ≠ –1) is

If the area of the triangle whose vertices are (b, c), (c, a) and (a , b) is ∆, then the area of the triangle whose vertices are (ac – b², ab – c²), (ba – c², bc – a²), and (cb – a², ca – b²) is

Two vertices of a triangle are (5, –1) and (–2, 3). If the orthocentre of the triangle is at (0, 0), then the third vertex is

If (x₁, y₁), (x₂, y₂) and (x₃, y₃) are the co–ordinates of the circumcentre, the centroid and the orthocentre of a triangle, then