Vector Algebra questions
907 published questions with worked solutions.
- Let a unit vector u = x i + y j + z k make angles π/2, π/3 and 2π/3 with the vectors 1 2 i + 1 2 k, 1 2 j + 1 2 k and 1 2 i + 1 2...
- Let O be the origin, and M and N be the points on the lines x-5 4 = y-4 1 = z-5 3 and x+8 12 = y+2 5 = z+11 9 respectively such...
- Let O be the origin and the position vectors of A and B be 2 i + 2 j + k and 2 i + 4 j + 4 k respectively. If the internal...
- Let a, b and c be three non-zero vectors such that b and c are non-collinear. If a + 5 b is collinear with c, b + 6 c is...
- Let a⃗ and b⃗ be two vectors such that |b⃗| = 1 and |b⃗ × a⃗| = 2. Then |(b⃗ × a⃗) − b⃗|² is equal to
- Let a = i + j + k, α, β ∈ ℝ. Let a vector b⃗ be such that the angle between a⃗ and b⃗ is π/4 and |b⃗|² = 6. If a⃗·b⃗ = 3√2, then...
- Let A(2, 3, 5) and C(–3, 4, –2) be opposite vertices of a parallelogram ABCD. If the diagonal BD = i + 2 j + 3 k, then the area...
- Let a = a_1 i + a_2 j + a_3 k and b = b_1 i + b_2 j + b_3 k be two vectors such that |a⃗| = 1, a⃗·b⃗ = 2 and |b⃗| = 4. If c = 2(...
- If d₁ is the shortest distance between the lines x + 1 = 2y = –12z, x = y + 2 = 6z – 6 and d₂ is the shortest distance between...
- The shortest distance between lines L₁ and L₂, where L₁ : (x − 1)/2 = (y + 1)/(−3) = (z + 4)/2 and L₂ is the line, passing...
- Let a⃗ = 3î + 2ĵ + k̂, b⃗ = 2î − ĵ + 3k̂ and c⃗ be a vector such that (a⃗ + b⃗) × c⃗ = 2(a⃗ × b⃗) + 24ĵ − 6k̂ and (a⃗ − b⃗ +...
- Let a⃗ = 3î + ĵ − 2k̂, b⃗ = 4î + ĵ + 7k̂ and c⃗ = î − 3ĵ + 4k̂ be three vectors. If a vector p⃗ satisfies p⃗ × b⃗ = c⃗ × b⃗ and...
- Let a⃗ and b⃗ be two vectors such that |a⃗| = 1, |b⃗| = 4, and a⃗·b⃗ = 2. If c⃗ = (2a⃗ × b⃗) − 3b⃗ and the angle between b⃗ and...
- Let a =2 i - j +2 k and b = i +2 j - k .r Let a vector v be in the plane containing a and b . If v is perpendicular to the vector...
- If the foot of the perpendicular from point (4, 3, 8) on the line L_1: x-a = y-2 3 = z-b 4 , 0 is (3, 5, 7), then the shortest...
- Let a = i +2 j -3 k and b =2 i -3 j +5 k . If r a = b r , r .( i +2 j + k )=3 and r .(2 i +5 j - k )=-1, R, then the value of +|...
- Let c be a vector perpendicular to the vectors a = i + j - k and b = i +2 j + k . If c .( i + j +3 k )=8 then the value of c .( a...
- Let a vector i + j be obtained by rotating the vector 3 i + j by an angle 45° about the origin in counterclockwise direction in...
- Let the position vectors of two points P and Q be 3 i - j +2 k and i +2 j -4 k , respectively. Let R and S be two points such...
- Let O be the origin. Let OP =x i +y j - k and OQ =- i +2 j +3x k , x, y R, x > 0, be such that | PQ |= 20 and the vector OP is...
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