Triangle PQR, Points A, B, C Divide Sides in Ratio 1:2, Find Area(PQR)/Area(ABC)
Let PQR be a triangle. Points A, B, C are on sides QR, RP, PQ such that QA/AR = RB/BP = PC/CQ = 1/2. Find Area(PQR)/Area(ABC) using position vectors.
-
-
Distance From C to Angle Bisector of OA, OB is 9/√2, Find a
Three points given by position vectors, a distance from an angle bisector — solved fastest by switching to plain coordinate geometry. JEE Main 2025.
-
Position Vectors 4p+q-3r, -5p+q+2r, 2p-q+2r: Find α+2β+5γ
A JEE Main 2025 vector geometry problem solved using the Euler line property that the centroid divides the orthocenter-circumcenter segment 2:1.
-
Unit Vector Perpendicular to b, c at Angles cos⁻¹(-1/3) and π/3
Find alpha when a unit vector perpendicular to two given vectors also satisfies two angle conditions. A JEE Main 2025 3D vector problem, solved fully.