Vector Algebra questions
907 published questions with worked solutions.
- If a = i - 2 j + 3 k, b = 2 i + 3 j - k and c = r i + j + (2r - 1) k are three vectors such that c is parallel to the plane of a...
- Statement 1: The vectors a, b and c lie in the same plane if and only if a ( b c) = 0 Statement 2: The vectors u and v are...
- Let â and b̂ be two unit vectors. If the vectors c = a + 2 b and d = 5 a - 4 b are perpendicular to each other, then the angle...
- Let ABCD be a parallelogram such that AB = q, AD = p and ∠BAD be an acute angle. If r is the vector that coincides with the...
- Let a = 2 i - j + k, b = i + 2 j - k and c = i + j - 2 k be three vectors. A vector of the type b + c for some scalar λ, whose...
- The vector ( i ( a b)) i + ( j ( a b)) j + ( k ( a b)) k is equal to:
- A vector n is inclined to x-axis at 45°, to y-axis at 60° and at an acute angle to z-axis. If n is a normal to a plane passing...
- If â, b̂ and ĉ are unit vectors satisfying a - 3 b + c = 0, then the angle between the vectors â and ĉ is :
- If a and b are non-collinear vectors, then the value of α for which the vectors u = ( - 2) a + b and v = (2 + 3 ) a - 3 b are...
- Let a = 2 i + j - 2 k, b = i + j. If c is a vector such that a c = | c|, | c - a| = 2 2 and the angle between a b and c is 30°,...
- If | a| = 2, | b| = 3 and |2 a - b| = 5, then |2 a + b| equals :
- If | c|^2 = 60 and c ( i + 2 j + 5 k ) = 0, then a value of c (-7 i + 2 j + 3 k ) is:
- If x, y and z are three unit vectors in threedimensional space, then the minimum value of | x + y|^2 + | y + z|^2 + | z + x|^2
- If x = 3 i - 6 j - k, y = i + 4 j - 3 k and z = 3 i - 4 j - 12 k, then the magnitude of the projection of x y on z is
- Equation of the line of the shortest distance between the lines x1 = y -1 = z1 and x-1 0 = y+1 -2 = z1 is
- For real numbers α, β, γ, δ and µ, consider the matrix M = bmatrix & 1 2 & - 1 2 1 3 & & 1 3 & & bmatrix . Suppose that MM^T = I,...
- Let a, b be two vectors, and let P, Q and R be the points with position vectors a, b and a+ b, respectively, with respect to the...
- The position vector of a point P is r=x i+y j+z k, where x N , y N , z N and a= i+ j+ k. If r a=10, the number of possible...
- ABCDEF is a regular hexagon where centre O is the origin. If the position vectors of A and B are i - j + 2 k and 2 i + j + k...
- Let the position vectors of the points A, B, C be i + 2 j + 3 k, - i - j + 8 k and -4 i + 4 j + 6 k respectively. Then the ABC 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