Vector Algebra questions
907 published questions with worked solutions.
- If _1< _2 are two values of such that the angle between the planes P_1: r (3 i -5 j + k )=7 and P_2: r ( i + j -3 k )=9 is ^ -1 (...
- Let a = i +2 j +3 k , b = i - j +2 k and c =5 i -3 j +3 k be three vectors if r is a vector such that r b = c b and r . a =0,...
- Let a , b , c be three vectors such that | a |= 31 , 4| b |=| c |=2 and 2( a b )=3( c a ). If the angle between b and c is 2 3 ,...
- Let the shortest distance between the line L : x-5 -2 = y- 1 = z+ 1 , 0 and L_1 : x + 1 = y – 1 = 4 – z be 2 6. If ( , , ) lies...
- Let a =2 i + j + k and b and c be two nonzero vectors such that | a + b + c |=| a + b - c | and b . c =0. Consider the following...
- Let be the angle between the planes P_1: r .( i + j +2 k )=9 and P_2: r .(2 i - j + k )=15. Let L be the line that meets P_2 at...
- Let a and b be two vectors such that | a |= 14 | b |= 6 and | a b |= 48 . Then ( a . b )^2 is equal to________.
- The number of distinct real values of λ, for which the vectors - ^2 i + j + k, i - ^2 j + k and i + j - ^2 k are coplanar, is
- Let the vectors PQ , QR , RS , ST , TU and UP represent the sides of a regular hexagon. STATEMENT-1 : PQ ( RS + ST ) 0. because...
- Let a, b, c be unit vectors such that a + b + c = 0. Which one of the following is correct?
- Let two non-collinear unit vectors a and b form an acute angle. A point P moves so that at any time t the position vector OP...
- If a, b, c and d are unit vectors such that ( a b) ( c d) = 1 and a c = 1 2 , then
- For any two points M and N in the XY-plane, let MN denote the vector from M to N, and 0 denote the zero vector. Let P, Q and R be...
- If | a| = 4, | b| = 2 and the angle between a and b is /6 then ( a b)^2 = 2 is equal to
- If a, b, c are vectors such that [ a b c] = 4 then [ a b b c c a] =
- If a, b, c are vectors such that a + b + c = 0 and | a| = 7, | b| = 5, | c| = 3 then angle between vector b and c is
- If |a| = 5, |b| = 4, |c| = 3 thus what will be the value of |a b + b c + c a|, given that a + b + c = 0
- 3 c + 2 ( a b) = 0 then
- If a b = b c = c a then a + b + c =
- Let u = i + j, v = i - j and w = i + 2 j + 3 k. If n is a unit vector such that u n = 0 and v n = 0, then | w n| is equal to
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