Vector Algebra questions
907 published questions with worked solutions.
- Let a, b, c R be such that a^2+b^2+c^2=1. If a =b ( + 2 3 )=c ( + 4 3 ), where = 9 , then the angle between the vectors a i +b j...
- Let a = i + j + k, b = - i - 8 j + 2 k and c = 4 i + c_2 j + c_3 k, be three vectors such that b a = c a. If the angle between...
- Let a = -5 i + j - 3 k, b = i + 2 j - 4 k and c = ((( a b) i) i) i. Then c (- i + j + k) is equal to:
- If the shortest distance between the lines x - -2 = y - 2 1 = z - 1 1 and x - 3 1 = y - 1 -2 = z - 2 1 is 1, then the sum of all...
- Let the line of the shortest distance between the lines L_1 : r = ( i + 2 j + 3 k) + ( i - j + k) and L_2 : r = (4 i + 5 j + 6 k)...
- If λ > 0, let θ be the angle between the vectors a = i + j - 3 k and b = 3 i - j + 2 k. If the vectors a + b and a - b are...
- Let a = i + j + k, b = 2 i + 4 j - 5 k and c = x i + 2 j + 3 k, x ∈ R. If d is the unit vector in the direction of b + c such...
- Let a unit vector which makes an angle of 60º with 2 i + 2 j - k and an angle of 45º with i - k be C. Then C + (- 12 i + 1 3 2 j...
- If the shortest distance between the lines x + 2 2 = y + 3 3 = z - 5 4 and x - 3 1 = y - 2 -3 = z + 4 2 is 38 3 5 k and...
- Let ABC be a triangle of area 15√2 and the vectors AB = i + 2 j - 7 k, BC = a i + b j + c k and AC = 6 i + d j - 2 k, d > 0. Then...
- Let a = i - 3 j + 7 k, b = 2 i - j + k and c be a vector such that ( a + 2 b) c = 3( c a). If a c = 130, then b c is equal to...
- Let a = 2 i + 5 j - k, b = 2 i - 2 j + 2 k and c be three vectors such that ( c + i) ( a + b + i) = a ( c + i), a c = -29, then c...
- Consider three vectors a, b, c. Let | a| = 2, | b| = 3 and a = b c. If α ∈ [0, 3 ] is the angle between the vectors b and c, then...
- Let the point (−1, α, β) lie on the line of the shortest distance between the lines x + 2 -3 = y - 2 4 = z - 5 2 and x + 2 -1 = y...
- The shortest distance between the lines x - 3 2 = y + 15 -7 = z - 9 5 and x + 1 2 = y - 1 1 = z - 9 -3 is
- Let αβγ = 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 ∈ R, xyz ≠ 0, then 6α + 4β + γ is...
- Let a = 2 i - 3 j + 4 k, b = 3 i + 4 j - 5 k and a vector c be such that a ( b + c) + b c = i + 8 j + 13 k. If a c = 13, then (24...
- A vector a = i +2 j + k ( , R) lies in the plane of the vectors, b = i + j and c = i - j +4 k . If a bisects the angle between b...
- The shortest distance between the lines x-3 3 = y-8 -1 = z-3 1 and x+3 -3 = y+7 2 = z-6 4 is -
- Let the volume of a parallelopiped whose coterminous edges are given by u = i + j + k , v = i + j +3 k and w =2 i + j + k be 1...
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