Vector Algebra questions
907 published questions with worked solutions.
- The position vectors of the points A, B, C are i+2 j- k, i+ j+ k, 2 i+3 j+2 k respectively. If A is chosen as the origin, then...
- If the area of a parallelogram whose diagonals are represented by vectors 3 i+ j+2 k and i-2 j+3 k is 117 2 sq. units, then =
- If a= i+ j+ k, b= j- k then a vector c such that a c= b and a c=3 is
- The vectors a , b and c are such that | a |=2,| b |=4,| c |=4. If the projection of b on a is equal to projection of c on a and b...
- The values of x for which the angle between the vectors a =2x^2 i +4x j + k and b =7 i -2 j +x k is obtuse, are
- If a , b , c are three coplanar vectors such that | a |=1,| b |=2, b c =8 and the angle between b and c is 45^0 then the value of...
- The unit vectors perpendicular to the plane determined by the points A (1, -1, 2) B (2, 0, -1) C (0, 2, 1) is
- The volume of tetrahedron with co-terminus edges a , b , c is 64 3 cubic units, then volume of parallelepiped considering...
- If a, b, c are three coplanar vectors such that | a|=1, | b|=2, b c=8, the angle between b and c is 45^0, then = | a ( b c) |=
- Let a, b and c be vectors of magnitude 2, 3 and 4 respectively. If a is perpendicular to ( b+ c ), b is perpendicular to ( c+ a )...
- If a= x i+y j+4z k, b=y i+x j+3y k, c=-z i-2z j-( +1)x k, are the sides of the triangle ABC, where x, y, z are not all zero, such...
- ABCD is a quadrilateral with AB = a, AD = b, and AC =2 a+3 b. If its area is times the area of the parallelogram with AB, AD as...
- If c=5 a+6 b and 3 c= a-4 b then
- The vectors p= i+a j+a^2 k, q= i+b j+b^2 k and r= i+c j+c^2 k are non-coplanar and vmatrix a&a^2&1+a^3 &b^2&1+b^3 &c^2&1+c^3...
- Two adjacent sides of a parallelogram ABCD are given by AB =2 i+10 j+11 k and AD =- i+2 j+2 k. The side AD is rotated by an acute...
- If a = i - 2 j + 3 k, b = 2 i + 3 j - k and c = i + j + (2 - 1) k are coplanar vectors, then λ is equal to
- If u = j + 4 k, v = i + 3 k and w = i + j are vectors in 3-dimensional space, then the maximum possible value of | u v w| is
- A unit vector which is perpendicular to the vector 2 i - j + 2 k and is coplanar with the vectors i + j - k and 2 i + 2 j - k is
- If a + b + c = 0, | a| = 3, | b| = 5 and | c| = 7, then the angle between a and b is
- Statement 1: The shortest distance between the lines x2 = y -1 = z2 and x - 1 4 = y - 1 -2 = z - 1 4 is 2. Statement 2: The...
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