PrepWiser › Learn › Mathematics › VectorsVectors — JEE Main PYQs & Practice Questions Vectors is a Mathematics chapter in the JEE Main syllabus. This page brings together 212 previous-year and practice questions on Vectors, organised into 6 topics: Types of Vectors, Dot and Cross Product, Scalar Triple Product, Vector Triple Product, Vector Equation of Line and Coplanarity and Collinearity. Most questions come with a step-by-step solution you can work through free in PrepWiser.
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Types of Vectors Dot and Cross Product Let a⃗ = a₁î + a₂ĵ + a₃k̂ aᵢ > 0, i = 1,2,3 be a vector which makes equal angles with… Let three vectors ,a⃗=α î+4 ĵ+2 k̂, b⃗=5 î+3 ĵ+4 k̂, c⃗=x î+y ĵ+z k̂ form a triangle… Let A B C D be a tetrahedron such that the edges A B, A C and A D are mutually… Let a⃗=a₁ î+a₂ ĵ+a₃ k̂ and b⃗=b₁ î+b₂ ĵ+b₃ k̂ be two vectors such that |a⃗|=1, a⃗ · b⃗=2… Consider a △ A B C where A(1,3,2), B(-2,8,0) and C(3,6,7). If the angle bisector of ∠ B… Let A(2,3,5) and C(-3,4,-2) be opposite vertices of a parallelogram A B C D. If the… The set of all α, for which the vectors a⃗=α t î+6 ĵ-3 k̂ and b⃗=t î-2 ĵ-2 α t k̂ are… Let a⃗ and b⃗ be two vectors such that |b⃗|=1 and |b⃗ × a⃗|=2. Then |(b⃗ × a⃗)-b⃗|² is… A(2,6,2), B(-4,0, λ), C(2,3,-1) and D(4,5,0),|λ| ≤ 5 are the vertices of a quadrilateral… For a triangle ABC, let p⃗=BC⃗,q⃗=CA⃗ and r⃗=BA⃗. If |p⃗|=2√3,|q⃗|=2 and cos θ=1/√3… The area of the quadrilateral ABCD with vertices A(2,1,1), B(1,2,5), C(-2,-3,5) and… Let a⃗ = 2î - 3ĵ + 4k̂ and b⃗ = 7î + ĵ - 6k̂. If r⃗ × a⃗ = r⃗ × b⃗, r⃗ . (î + 2ĵ + k̂) =… In a triangle ABC, if | BC⃗ | = 3, | CA⃗ | = 5 and | BA⃗ | = 7, then the projection of… Let a and b be two unit vectors such that the angle between them is π/4. If θ is the… Let a and b be two unit vectors such that |(a + b) + 2(a × b)| = 2. If θ ∈ (0, π) is the… An arc PQ of a circle subtends a right angle at its centre O. The mid point of the arc… Let P(3,2,3), Q(4,6,2) and R(7,3,2) be the vertices of △ PQR. Then, the angle ∠ QPR is Let a⃗=î+ĵ+k̂, b⃗=-î-8 ĵ+2 k̂ and c⃗=4 î+c₂ ĵ+c₃ k̂ be three vectors such that b⃗ ×… Let a⃗=î+2 ĵ+k̂, b⃗=3 î-3 ĵ+3 k̂, c⃗=2 î-ĵ+2 k̂ and d⃗ be a vector such that b⃗ × d⃗=c⃗… Let x⃗ be a vector in the plane containing vectors a⃗ = 2î - ĵ + k̂ and b⃗ = î + 2ĵ -… Scalar Triple Product If the volume of a parallelopiped, whose coterminus edges are given by the vectors a⃗ =… Let a⃗=î+ĵ+k̂, b⃗=2 î+4 ĵ-5 k̂ and c⃗=x î+2 ĵ+3 k̂, x ∈ ℝ. If d⃗ is the unit vector in… Let a⃗ = î + ĵ + k̂ and b⃗ = ĵ - k̂. If c⃗ is a vector such that a⃗ × c⃗ = b⃗ and a⃗ .c⃗… Let the volume of a parallelopiped whose coterminous edges are given by u⃗ = î + ĵ + λ… If the vectors, p⃗ = ( a + 1 )î + aĵ + ak̂, q⃗ = aî + ( a + 1 )ĵ + ak̂ and r⃗ = aî + aĵ… Let a⃗, b⃗, c⃗ be three coplanar concurrent vectors such that angles between any two of… If a⃗ = α î + β ĵ + 3k̂, b⃗ = - β î - α ĵ - k̂ and c⃗ = î - 2ĵ - k̂ such that a⃗ . b⃗ =… Let the position vectors of the vertices A, B and C of a tetrahedron ABCD be î+2 ĵ+k̂… Let a⃗ = î - α ĵ + β k̂, b⃗ = 3î + β ĵ - α k̂ and c⃗ = -α î - 2ĵ + k̂, where α and β are… Let c⃗ be a vector perpendicular to the vectors, a⃗ = î + ĵ - k̂ and b⃗ = î + 2ĵ + k̂… Let the vectors a⃗, b⃗, c⃗ represent three coterminous edges of a parallelopiped of… Let the vectors (2 + a + b)î + (a + 2b + c)ĵ - (b + c)k̂,(1 + b)î + 2bĵ - bk̂ and (2 +… Let x₀ be the point of Local maxima of f(x) = a⃗ .( b⃗ × c⃗ ), where a⃗ = xî - 2ĵ + 3k̂… If four distinct points with position vectors a⃗, b⃗, c⃗ and d⃗ are coplanar, then [a⃗… Let the vectors u⃗₁=î+ĵ+a k̂, u⃗₂=î+b ĵ+k̂ and u⃗₃=c î+ĵ+k̂ be coplanar. If the vectors… Let v⃗=α î+2 ĵ-3 k̂, w⃗=2 α î+ĵ-k̂ and u⃗ be a vector such that |u⃗|=α>0. If the minimum… If a⃗ . b⃗ = 1, b⃗ . c⃗ = 2 and c⃗ . a⃗ = 3, then the value of [ a⃗ × ( b⃗ × c⃗ ), b⃗ ×… Let a vector a⃗ be coplanar with vectors b⃗ = 2î + ĵ + k̂ and c⃗ = î - ĵ + k̂. If a⃗ is… Vector Triple Product Let a⃗ = î + ĵ + 2k̂ and b⃗ = - î + 2ĵ + 3k̂. Then the vector product ( a⃗ + b⃗ ) × ( (… If a⃗=î+ĵ+k̂,b⃗=ĵ-k̂ and c⃗ be three vectors such that a⃗× c⃗=b⃗ and a⃗· c⃗=3, then c⃗·… If a⃗ ,b⃗ ,c⃗ are three non-zero vectors and n is a unit vector perpendicular to c⃗ such… Let a⃗=3 î+ĵ and b⃗=î+2 ĵ+k̂. Let c⃗ be a vector satisfying a⃗ ×(b⃗ × c⃗)=b⃗+λ c⃗. If b⃗… Let a⃗=-î+ĵ+2k̂,b⃗=î-ĵ-3k̂,c⃗=a⃗× b⃗ and d⃗=c⃗× a⃗. Then (a⃗-b⃗)· d⃗ is equal to : Let a vector c⃗ be coplanar with the vectors a⃗ = - î + ĵ + k̂ and b⃗ = 2î + ĵ - k̂. If… Let a⃗, b⃗ and c⃗ be three vectors such that a⃗ = b⃗ × (b⃗ × c⃗). If magnitudes of the… Let a⃗ ,b⃗ ,c⃗ three vectors mutually perpendicular to each other and have same… Let a⃗=2 î-ĵ+5 k̂ and b⃗=α î+β ĵ+2 k̂ . If ((a⃗ × b⃗) × î) · k̂=23/2 , then |b⃗ × 2 ĵ|… Let a⃗, b⃗ and c⃗ be three vectors such that | a⃗ | = √3, | b⃗ | = 5,b⃗ .c⃗ = 10 and the… Vector Equation of Line Coplanarity and Collinearity If the four points, whose position vectors are 3î - 4ĵ + 2k̂,î + 2ĵ - k̂, - 2î - ĵ + 3k̂… Let S be the set of all (λ, μ) for which the vectors λ î-ĵ+k̂, î+2 ĵ+μ k̂ and 3 î-4 ĵ+5… If the vectors a⃗ = λ î + μ ĵ + 4k̂, b⃗ = - 2î + 4ĵ - 2k̂ and c⃗ = 2î + 3ĵ + k̂ are… Let α β γ=45 ; α, β, γ ∈ ℝ. If x(α, 1,2)+y(1, β, 2)+z(2,3, γ)=(0,0,0) for some x, y, z ∈… Let a⃗, b⃗ and c⃗ be three non-zero non-coplanar vectors. Let the position vectors of… The sum of all values of α, for which the points whose position vectors are î-2 ĵ+3 k̂… Let a, b and c be distinct positive numbers. If the vectors aî + aĵ + ck̂,î+k̂ and cî +… Let the position vectors of the points A, B, C and D be 5 î+5 ĵ+2 λ k̂, î+2 ĵ+3 k̂,-2… If (2,3,9),(5,2,1),(1, λ, 8) and (λ, 2,3) are coplanar, then the product of all possible… If a⃗ = 2î + ĵ + 3k̂, b⃗ = 3î + 3ĵ + k̂ and c⃗ = c₁î + c₂ĵ + c₃k̂ are coplanar vectors… If (1, 5, 35), (7, 5, 5), (1, λ, 7) and (2λ, 1, 2) are coplanar, then the sum of all… Let the vectors a⃗=(1+t) î+(1-t) ĵ+k̂, b⃗=(1-t) î+(1+t) ĵ+2 k̂ and c⃗=t î-t ĵ+k̂, t ∈ R… Let the arc A C of a circle subtend a right angle at the centre O. If the point B on the… If the points with position vectors α î+10 ĵ+13 k̂, 6 î+11 ĵ+11 k̂, 9/2 î+β ĵ-8 k̂ are… Let a⃗, b⃗ and c⃗ be three non-zero vectors such that b⃗ and c⃗ are non-collinear. If… Let a, b, c be three distinct real numbers, none equal to one. If the vectors a î+ĵ+k̂… Let O be the origin. Let OP⃗ = xî + yĵ - k̂ and OQ⃗ = - î + 2ĵ + 3xk̂, x, y∈R, x > 0, be… More Mathematics chapters Frequently asked questions How many Vectors questions are there for JEE Main? PrepWiser has 212 Vectors questions for JEE Main, grouped into 6 topics such as Types of Vectors, Dot and Cross Product and Scalar Triple Product.
Are these Vectors questions from previous-year JEE Main papers? Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.
Where can I see the answers and solutions to these Vectors questions? Open any Vectors question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.