JEE Main 2025 — Vector Algebra Questions with Solutions

Let a=i+j+k, b=2 i+2 j+k and d=a × b. If c is a vector such that a · c=|c|, |c-2 a|²=8 and the angle between d and c is…

Let a=3 i-j+2 k, ~b=a ×(i-2 k) and c=b × k. Then the projection of c-2 j on a is :

Let a be a unit vector perpendicular to the vectors b=i-2 j+3 k and c=2 i+3 j-k, and makes an angle of ⁻¹ (-(1)/(3) ) w…

If the components of a=α i+β j+γ k along and perpendicular to b=3 i+j-k respectively, are (16)/(11)(3 i+j-k) and (1)/(1…

Let a and b be the vectors of the same magnitude such that |a+b|+|a-b||a+b|-|a-b|=√(2)+1. Then |a+b|²|a|² is :

Let A, B, C be three points in x y-plane, whose position vector are given by √(3) i+j, i+√(3) j and a i+(1-a) j respect…

Let a=i+2 j+k, b=3 i-3 j+3 k, c=2 i-j+2 k and d be a vector such that b × d=c × d and a · d=4. Then |(a × d)|² is equal…

Let the position vectors of the vertices A, B and C of a tetrahedron A B C D be i+2 j+k, i+3 j-2 k and 2 i+j-k respecti…

Let a and b be two unit vectors such that the angle between them is (π)/(3). If λ a+2 b and 3 a-λ b are perpendicular t…

Let the three sides of a triangle A B C be given by the vectors 2 i-j+k, i-3 j-5 k and 3 i-4 j-4 k. Let G be the centro…