JEE Main Mathematics — Vector Algebra Previous-Year Questions

If a and b are two vectors such that |a| = 2 and |b| = 3, then the maximum value of 3 | (3a + 2b ) | + 4 | (3a - 2b ) |…

For three unit vectors a, b, c satisfying |a-b|²+|b-c|²+|c-a|²=9 and |2 a+k b+k c|=3, the positive value of k is

Let a=i-2 j+3 k, b=2 i+j-k, c=λ i+j+k and v=a × b. If v · c=11 and the length of the projection of b on c is p, then 9…

Let a=2 i+j-2 k, b=i+j and c=a × b. Let d be a vector such that |d-a|=√(11),|c × d|=3 and the angle between c and d is…

Two adjacent sides of a parallelogram PQRS are given by PQ = j + k and PS = i - j. If the side PS is rotated about the…

Let a=2 i-j-k, b=i+3 j-k and c=2 i+j+3 k. Let v be the vector in the plane of the vectors a and b, such that the length…

Let a = 2i + 3j + 3k and b = 6i + 3j + 3k. Then the square of the area of the triangle with adjacent sides determined b…

For a triangle ABC, let p=BC, q=CA and r=BA. If |p|=2 √(3),|q|=2 and θ=1√(3), where θ is the angle between p and q, the…

Let AB=2 i+4 j-5 k and AD=i+2 j+λ k, λ R. Let the projection of the vector v=i+j+k on the diagonal AC of the parallelog…

Let the vectors a = -i + j + 3k and b = i + 3j + k. For some λ, µ R, let c = λ a + µ b. If c · (3i - 6j + 2k) = 10 and…