Vector Algebra questions
907 published questions with worked solutions.
- The shortest distance between the lines (x − 3)/2 = (y − 2)/3 = (z − 1)/(−1) and (x + 3)/2 = (y − 6)/1 = (z − 5)/3, is
- Let a and b be the vectors along the diagonals of a parallelogram having area 2 2 . Let the angle between a and b be acute, | a |...
- Let a = i + j - k and c = 2 i - 3 j + 2 k . then the number of vectors b such that b c = a and | b | 1, 2, _____, 10 is :
- Let the vectors a = (1 + t) i + (1 - t) j + k , b = (1 - t) i + (1 + t) j + 2 k and c = t i - t j + k , t R be such that for , ,...
- Let a vector a has magnitude 9. Let a vector b be such that for every (x, y) R R − (0, 0) , the vector (x a + y b ) is...
- Let a = i + 2 j - k and b = -2 i + j + k , where R. If the area of the parallelogram whose adjacent sides are represented by the...
- Let the plane P : r a = d contain the line of intersection of two planes r ( i + 3 j - k ) = 6 and r (-6 i + 5 j - k ) = 7. If...
- If a = 2 i + j + 3 k , b = 3 i + 3 j + k and c = c_ 1 i + c_ 2 j + c_ 3 k are coplanar vectors, a c = 5, b c then 122(c_ 1 + c_ 2...
- If (2, 3, 9), (5, 2, 1), (1, , 8) and ( , 2, 3) are coplanar, then the product of all possible values of is:
- Let a , b , c be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their...
- Let a and b be two vectors such that | a + b |^ 2 = | a |^ 2 + 2| b |^ 2 , a b = 3 and | a b |^ 2 = 75. Then | a |^ 2 is equal to...
- Let a = 3 i + j and b = i + 2 j + k . Let c be a vector satisfying a ( b c ) = b + c . If b and c are non-parallel, then the...
- Let a and b be two unit vectors such that the angle between them is /4. If is the angle between the vectors ( a + b ) and ( a + 2...
- Let a = i - 2 j + 3 k , b = i - j - k and c be a vector such that a + ( b c ) = 0 and b c = 5. Then the value of 3( c a ) is...
- If a = i -2 j +5 k and b =2 i + j -3 k then what is ( b - a ) (3 a + b ) equal to?
- If the position vectors of points A and B are 3 i -2 j + k and 2 i +4 j -3 k respectively, then what is the length of AB ?
- The sine of the angle between vectors a =2 i -6 j -3 k and b =4 i +3 j - k is
- What is the value of for which the vectors 3 i +4 j - k and -2 i + j +10 k are perpendicular?
- Consider the vectors x = i + 2 j + 3 k, y = 2 i + 3 j + k, and z = 3 i + j + 2 k. For two distinct positive real numbers α and β,...
- Let the position vectors of the points A, B, C and D be 5 i +5 j +2 k , i +2 j +3 k , -2 i + j +4 k and - i +5 j +6 k . Let the...
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