Vector Algebra questions
907 published questions with worked solutions.
- Let a = i + j + k , c = j - k and a vector b be such that a b = c and a b = 3. Then | b | equals ?
- The magnitude of the projection of the vector 2 i + 3 j + k on the vector perpendicular to the plane containing the vectors i + j...
- Let a = 3 i + 2 j + x k and b = i - j + k, for some real x. Then | a b| = r is possible if:
- Let = 3 i + j and = 2 i - j + 3 k. If = _1 - _2, where _1 is parallel to and _2 is perpendicular to , then _1 _2 is equal to:
- If a , b and c are unit vectors such that a + 2 b + 2 c = 0 , then | a c | is equal to
- If the position vectors of the vertices A, B and C of a are respectively 4 i + 7 j + 8 k , 2 i + 3 j + 4 k and 2 i + 5 j + 7 k ,...
- Let a = i + j + 2 k, b = b_1 i + b_2 j + 2 k and c = 5 i + j + 2 k be three vectors such that the projection vector of b on a is...
- Let a = i - j, b = i + j + k and c be a vector such that a c + b = 0 and a c = 4, then | c|^2 is equal to:
- Let a = 3 i + 2 j + 2 k and b = i + 2 j - 2 k be two vectors. If a vector perpendicular to both the vectors a + b and a - b has...
- If the volume of parallelopiped formed by the vectors i + j + k, j + k and i + k is minimum, then λ is equal to:
- Let a, b and c be three unit vectors, out of which vectors b and c are non-parallel. If α and β are the angles which vector a...
- The sum of the distinct real values of μ, for which the vectors, i + j + k, i + j + k, i + j + k are co-planar, is:
- Let a = i + 2 j + 4 k, b = i + j + 4 k and c = 2 i + 4 j + ( ^2 - 1) k be coplanar vectors. Then the non-zero vector a c is:
- If = ( - 2) a + b and = (4 - 2) a + 3 b be two given vectors where vectors a and b are non-collinear. The value of λ for which...
- Let a = 2 i + _1 j + 3 k, b = 4 i + (3 - _2) j + 6 k, and c = 3 i + 6 j + ( _3 - 1) k be three vectors such that b = 2 a and a is...
- Let A be a point on the line r = (1 - 3 ) i + ( - 1) j + (2 + 5 ) k and B(3, 2, 6) be a point in the space. Then the value of μ...
- Let α ∈ R and the three vectors a = i + j + 3 k, b = 2 i + j - k and c = i - 2 j + 3 k. Then the set S = α : a, b and c are...
- Let a , b and c be three unit vectors such that a + b + c = 0 . If = a b + b c + c a and d = a b + b c + c a , then the ordered...
- Let a , b and c be three vectors such that | a |= 3 , | b |=5, b c =10 and the angle between b and c is 3 . If a is perpendicular...
- If the vectors, p =(a+1) i +a j +a k , q =a i +(a+1) j +a k and r =a i +a j +(a+1) k (a R) are coplanar and 3( p q )^2- | r q...
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