Vector Algebra questions
907 published questions with worked solutions.
- Let b = i + j + k , ℝ. If a is a vector such that a b = 13 i - j - 4 k and a b + 21 = 0, then ( b - a ) ( k - j ) + ( b + a ) ( i...
- Let l_ 1 be the line in xy-plane with x and y intercepts 1/8 and 1/(4 2 ) respectively and l_ 2 be the line in zx-plane with x...
- Let a = a_ 1 i + a_ 2 j + a_ 3 k , a_ i > 0, i = 1, 2, 3 be vector which makes equal angles with the coordinate axes OX, OY and...
- Let be the angle between the vectors a and b , where | a | = 4, | b | = 3 and ( /4, /3). Then |( a - b ) ( a + b )|^ 2 + 4( a b...
- A vector a is parallel to the line of intersection of the plane determined by the vectors i , i + j and the plane determined by...
- The largest value of a, for which the perpendicular distance of the plane containing the lines r = ( i + j ) + ( i + a j - k )...
- Let a = i + j - k and b = 2 i + j - k , > 0. If the projection of a b on the vector - i + 2 j - 2 k is 30, then is equal to
- If the lines r = ( i - j + k ) + (3 j - k ) and r = ( i - j ) + (2 j - 3 k ) are co-planar, then the distance of the plane...
- Let a = i + j + 2 k , b = 2 i - 3 j + k and c = i - j + k be three given vectors. Let v be a vector in the plane of a and b whose...
- If a b = 1, b c = 2 and c a = 3, then the value of [ a ( b c ), b ( c a ), c ( b a )] is
- Let a , b , c be three vectors mutually perpendicular to each other and same magnitude. If a vector r satisfies, a ( r - b ) a +...
- Let a =2 i -7 j +5 k , b = i + k , c = i +2 j -3 k be three given vectors. If r is a vector such that r a = c a and r b =0, then...
- Let a =5 i - j -3 k and b = i +3 j +5 k be two vectors. Then which one of the following statements is True?
- The shortest distance between the lines x-5 1 = y-2 2 = z-4 -3 and x+3 1 = y+5 4 = z-1 -5 is
- Let v =a i +2 j -3 k , w =2a i + j - k and u be a vector such that | u |= >0. If the minimum value of the scalar triple product |...
- Let the vectors a , b , c represent three coterminous edges of a parallelopiped of volume V. Then the volume of the...
- The sum of the all values of , for which the points whose position vectors are i -2 j +3 k , 2 i -3 j +4 k , ( +1) i +2 k , 9 i...
- Let P, Q, R and S be the points on the plane with position vectors -2 i - j, 4 i, 3 i + 3 j and -3 i + 2 j respectively. The...
- If a and b are vectors in space given by a = i - 2 j 5 and b = 2 i + j + 3 k 14 , then the value of (2 a + b ) [ ( a b ) ( a - 2...
- 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...
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