Vector Algebra questions
907 published questions with worked solutions.
- Let a = i + j + k, b = i - j + k and c = i - j - k be three vectors. A vector v in the plane of a and b, whose projection on c is...
- The vector(s) which is/are coplanar with vectors i + j + 2 k and i + 2 j + k, and perpendicular to the vector i + j + k is/are
- Let a = - i - k, b = - i + j and c = i + 2 j + 3 k be three given vectors. If r is a vector such that r b = c b and r a = 0, then...
- If a, b and c are unit vectors satisfying | a - b|^2 + | b - c|^2 + | c - a|^2 = 9, then |2 a + 5 b + 5 c| is
- If a and b are vectors such that | a + b| = 29 and a (2 i + 3 j + 4 k) = (2 i + 3 j + 4 k) b, then a possible value of ( a + b)...
- Let PR = 3 i + j - 2 k and SQ = i - 3 j - 4 k determine diagonals of a parallelogram PQRS and PT = i + 2 j + 3 k be another...
- Consider the set of eight vectors V = a i + b j + c k : a, b, c -1, 1 . Three non-coplanar vectors can be chosen from V in 2^p...
- Match List – I with List – II and select the correct answer using the code given below the lists : List – I P. Volume of...
- Let x, y and z be three vectors each of magnitude 2 and the angle between each pair of them is 3 . If a is a nonzero vector...
- Let a, b, and c be three non-coplanar unit vectors such that the angle between every pair of them is 3 . If a b + b c = p a + q b...
- Let PQR be a triangle. Let a = QR , b = RP and c = PQ . If | a |=12, | b |=4 3 and b c =24, then which of the following is (are)...
- Suppose that p , q and r are three non-coplanar vectors in R ^3. Let the components of a vector s along p , q and r be 4, 3 and...
- Let u =u_1 i +u_2 j +u_3 k be a unit vector in R ^3 and w = 1 6 ( i + j +2 k ). Given that there exists a vector v in R ^3 such...
- Let a and b be two unit vectors such that a b =0. For some x,y R , let c =x a +y b +( a b ). If | c |=2 and the vector c is...
- Consider the cube in the first octant with sides OP, OQ and OR of length 1, along the x-axis, y-axis and z-axis, respectively,...
- Three lines L_1: r = i , R , L_2: r = k + j , R and L_3: r = i + j +v k , v R are given. For which point(s) Q on L_2 can we find...
- Let a =2 i + j - k and b = i +2 j + k be two vectors. Consider a vector c = a + b , , R . If the projection of c on the vector (...
- For the equation of a line r = (-2 i + j + 3 k ) + t( i + 2 j - k ), t R, its Cartesian form is .........
- The vector equation of a line passes through the point A( i + j - 3 k ) and parallel to the line joining the points P(2 j - k )...
- The vector equation of the line passing through the points A( a ) and B( b ) is ..........
Other chapters
Alcohols, Phenols and EthersAldehydes, Ketones and Carboxylic AcidsAlternating CurrentAminesAnatomy of Flowering PlantsAncient Indian HistoryAnimal KingdomApplication of DerivativesArea Under CurveAromatic Compounds and Aryl HalidesAtomsBasic Mathematics and LogarithmBinomial TheoremBiodiversity and ConservationBiological ClassificationBiomoleculesBiotechnology and Its ApplicationsBiotechnology: Principles and ProcessesBody Fluids and CirculationBreathing and Exchange of GasesCell Cycle and Cell DivisionCell: The Unit of LifeChemical Bonding and Molecular StructureChemical Coordination and Integration