Three Dimensional Geometry questions
879 published questions with worked solutions.
- The plane containing the line x-1 1 = y-2 2 = z-3 3 and parallel to the line x1 = y1 = z4 passes through the point:
- A symmetrical form of the line of intersection of the planes x = ay + b and z = cy + d is
- If the angle between the line 2(x+1) = y = z + 4 and the plane 2x - y + z + 4 = 0 is 6, then the value of λ is
- Let P be the plane such that it contains the straight line x - 1 2 = y - 3 3 = z + 2 1 and is perpendicular to the plane x + 2y +...
- Let L be the straight line joining the points P(1,2,-1) and Q(2,3,1). Let S be the foot of the perpendicular drawn from the point...
- The coordinates of the point on the x-axis which is equidistant from the points (-3,4) and (2,5) are
- The position vectors of two vertices and the centroid of a triangle are i + j, 2 i - j + k and k respectively. The position...
- The coplanar points A, B, C, D are (2-x,2,2), (2,2-y,2), (2,2,2-z) and (1,1,1) respectively. Then
- The cosine of the angle between two diagonals of a cube is
- The distance of the point (1,1,1) from the plane passing through the points (2,1,1), (1,2,1) and (1,1,2) is
- The projection of the vector i+ j+ k on the line whose vector equation is r=(3+t) i+(2t-1) j+3t k, t being the scalar parameter,...
- A unit vector which is equally inclined to the vectors i, -2 i+ j+2 k 3 and -4 j-3 k 5 is
- A line makes angles , , with the positive directions of the axes of reference. The value of 2 + 2 + 2 is
- If a line makes angles of 60^ and 45^ with the positive directions of the x-axis and y-axis respectively then the acute angle...
- If is an angle given by = ^2 + ^2 + ^2 ^2 + ^2 + ^2 where , , are the angles made by a line with the positive directions of the...
- If the direction cosines of the line joining the origin and a point at unit distance from the origin are 1 3 , - 12, then the...
- The direction ratios of two parallel lines are 4, 3, -1 and + , 1 + , 2. The value of the pair ( , ) is
- The direction ratios of two perpendicular lines are 1, -3, 5 and , 1 + , 2 + . Then is
- The direction cosines of the line joining the points (2, 3, -1) and (3, -2, 1) are
- Let A = (2, 3, -1), B = (1, -1, 2). A point C on the y-axis such that AB BC has the coordinates
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