If Vector PO + OQ = Vector QO + OR, Prove That the Points P, Q, R Are Collinear
Prove P, Q, R are collinear given vector PO + OQ = vector QO + OR, by writing everything in position vectors and showing Q is the midpoint of P and R.
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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.
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Let A, B, C Have Position Vectors OA = √3i + j, OB = i + √3j and OC = ai + (1−a)j. If the Distance of C From the Line Bisecting the Angle Between OA and OB Is 9/√2, the Sum of All Possible Values of a Is
Three points given by position vectors, a distance from an angle bisector — solved fastest by switching to plain coordinate geometry. JEE Main 2025.
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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.
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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.