Vector Algebra questions
907 published questions with worked solutions.
- If u = i +2 j -2 k , v =2 i + k and w is unit vector then the maximum value of scalar triple product [ u v w ] is
- Let a =2 i + k , b = i + j + k , and c =4 i -3 j +7 k . If r is a vector such that r b = c b and r a =0. Then r c =
- Lines r = a + b and r = b + a intersect at point (2,4,-4). If | a - b |=4, then a b =
- If a , b and c are three vectors such that | a + b + c |=1, c = ( a b ) and | a |= 1 3 , | b |= 1 2 , | c |= 1 6 , then the angle...
- If a and b are unit vectors perpendicular to each other, Then [ a +( a b ) b +( a b ) ( a b )]=
- Let OD = i +2 j +6 k , CB =-3 i +2 k , be the diagonals of the parallelogram OBDC and OA = i +2 j +3 k be another vector. Then...
- The volume of the tetrahedron whose vertices are A(-1, 2, 3), B(3, -2, 1) C(p, 1, 3), D(-1, -2,4) is 16 3 cubic units then the...
- Let a = i + j + k , b = i -3 j +2 k and c =3 i -2 k . If a vector p satisfies the conditions p c =0 and p a = b a , then the...
- If M denotes the midpoint of the line joining A(4, 5, -10) and B( -1, 2, 1), then the equation of the plane through M and...
- 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
- a, b, c are nonzero vectors such that a is perpendicular to b and c, | a|=1, | b|=2, | c|=1 and b c=1. There is nonzero vector d...
- The value of m R, when angle between the vectors p=my i-6 j+3 k and q=y i+2 j+2my k is obtuse angle, is
- The volume of the tetrahedron whose coterminus edges are represented by a=-12 i+p k, b=3 j- k, c=2 i+ j-15 k, is 570 cu. units,...
- The shortest distance between the lines r = (4 i - j ) + ( i + 2 j - 3 k ) and r = ( i - j + 2 k ) + (2 i + 4 j - 5 k ) is
- Let a and b be unit vectors at an angle 3 with each other. If ( a ( b c ) ) ( a b ) = 5, then [ a b c ] =
- Let a, b and c be unit vectors. Suppose that a b = a c = 0 and if the angle between b and c is 6 , then a is
- If a and b are unit vectors such that | a + b| = 3, then the angle between a and b is
- Three vectors i - k, i + j + (1- ) k and i + j + (1+ - ) k represents conterminus edges of a parallelepiped, then the volume of...
- The line of intersection of the plane r (3 i - j + k ) = 1 and r ( i + 4 j - 2 k ) = 2 is parallel to the vector
- The distance of the plane r=( i- j)+ ( i+ j+ k)+ ( i-2 j+3 k) from the origin 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