JEE Advanced Vector Algebra — previous year questions

30 questions from 2026, 2025, 2024, 2023, 2022, 2021, 2020, 2019, 2018, 2015, 2014, 2013, 2012, 2011, 2010, 2009, 2008, 2007.

Let ā,b̄ be two vectors, and let P, Q and R be the points with position vectors ā,b̄ and ā+b̄,…2026JEE Advanced
For any two points M and N in the XY-plane, let M̅N̅ denote the vector from M to N, and 0̅ denote the zero…2025JEE Advanced
Consider the vectors x̄ = î + 2ĵ + 3k̂, ȳ = 2î + 3ĵ + k̂, and z̄ = 3î + ĵ + 2k̂. For two distinct…2025JEE Advanced
Let p = 2i + j + 3k and q = i - j + k. If for some real numbers α, β and γ, we have 15i + 10j + 6k = α(2p +…2024JEE Advanced
Let the position vectors of the points P, Q, R and S be ā = î + 2ĵ - 5k̂, b̄ = 3î + 6ĵ + 3k̂, c̄ =…2023JEE Advanced
Let î, ĵ and k̂ be the unit vectors along the three positive coordinate axes. Let \ a⃗ = 3î + ĵ - k̂, \…2022JEE Advanced
Let u⃗, v⃗ and w⃗ be vectors in three-dimensional space, where u⃗ and v⃗ are unit vectors which are not…2021JEE Advanced
Let O be the origin and OA⃗ = 2î + 2ĵ + k̂, OB⃗ = î - 2ĵ + 2k̂ and OC⃗ = 1/2(OB⃗ - λOA⃗) for some λ > 0.…2021JEE Advanced
Let a and b be positive real numbers. Suppose PQ⃗ = aî + bĵ and PS⃗ = aî - bĵ are adjacent sides of a…2020JEE Advanced
Let a⃗=2î+ĵ-k̂ and b⃗=î+2ĵ+k̂ be two vectors. Consider a vector c⃗=αa⃗+βb⃗,α,β∈ R. If the projection of…2019JEE Advanced
Let a⃗ and b⃗ be two unit vectors such that a⃗·b⃗=0. For some x,y∈R, let c⃗=xa⃗+yb⃗+(a⃗×b⃗). If |c⃗|=2 and…2018JEE Advanced
Suppose that p⃗, q⃗ and r⃗ are three non-coplanar vectors in R³. Let the components of a vector s⃗ along p⃗,…2015JEE Advanced
Let Δ PQR be a triangle. Let a⃗ = QR⃗, b⃗ = RP⃗ and c⃗ = PQ⃗. If |a⃗| = 12, |b⃗| = 4√3, b⃗ · c⃗ = 24, then…2015JEE Advanced
Let a⃗, b⃗ and c⃗ be three non-coplanar unit vectors such that the angle between every pair of them is π/3.…2014JEE Advanced
Let x⃗, y⃗ and z⃗ be three vectors each of magnitude √2 and the angle between each pair of them is π/3. If a⃗…2014JEE Advanced
Consider the set of eight vectors V = { a i + b j + c k : a, b, c ∈ {−1, 1} }. Three non-coplanar vectors can…2013JEE Advanced
If a⃗, b⃗ and c⃗ are unit vectors satisfying |a⃗-b⃗|² + |b⃗-c⃗|² + |c⃗-a⃗|² = 9, then |2a⃗+5b⃗+5c⃗| is2012JEE Advanced
If a and b are vectors such that |a+b| = √(29) and a × (2i+3j+4k) = (2i+3j+4k) × b, then a possible value of…2012JEE Advanced
Let a⃗=î+ĵ+k̂, b⃗=î-ĵ+k̂ and c⃗=î-ĵ-k̂ be three vectors. A vector v⃗ in the plane of a⃗ and b⃗, whose…2011JEE Advanced
Let a⃗=-î-k̂,b⃗=-î+ĵ and c⃗=î+2ĵ+3k̂ be three given vectors. If r⃗ is a vector such that r⃗×b⃗=c⃗×b⃗ and…2011JEE Advanced
The vector (s) which is/are coplanar with vectors î+ĵ+2k̂ and î+2ĵ+k̂, and perpendicular to the vector…2011JEE Advanced
Let P, Q, R and S be the points on the plane with position vectors -2î-ĵ, 4î, 3î+3ĵ and -3î+2ĵ…2010JEE Advanced
Two adjacent sides of a parallelogram ABCD are given by AB⃗ = 2î + 10ĵ + 11k̂ and AD⃗ = -î + 2ĵ + 2k̂ The…2010JEE Advanced
If a⃗ and b⃗ are vectors in space given by a⃗=(î-2ĵ)/√5 and b⃗=(2î+ĵ+3k̂)/√(14), then find the value of…2010JEE Advanced
If a⃗, b⃗, c⃗ and d⃗ are unit vectors such that (a⃗ × b⃗) · (c⃗ × d⃗) = 1 and a⃗ · c⃗ = 1/2, then2009JEE Advanced
Let two non-collinear unit vectors â and b̂ form an acute angle. A point P moves so that at any time t the…2008JEE Advanced
The edges of a parallelepiped are of unit length and are parallel to non-coplanar unit vectors â,b̂,ĉ such…2008JEE Advanced
Let a⃗,b⃗,c⃗ be unit vectors such that a⃗+b⃗+c⃗=0⃗. Which one of the following is correct ?2007JEE Advanced
The number of distinct real values of λ, for which the vectors -λ²î+ĵ+k̂, î-λ²ĵ+k̂ and î+ĵ-λ²k̂ are…2007JEE Advanced
Let the vectors PQ⃗, QR⃗, RS⃗, ST⃗, TU⃗ and UP⃗ represent the sides of a regular hexagon. STATEMENT I: PQ⃗ ×…2007JEE Advanced

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