Three Dimensional Geometry questions
879 published questions with worked solutions.
- Consider three planes P_1: x - y + z = 1, P_2: x + y - z = -1, P_3: x - 3y + 3z = 2. Let L_1, L_2, L_3 be the lines of...
- If the lines x-2 1 = y-3 1 = z-4 -k and x-1 k = y-4 2 = z-5 1 are coplanar, then k can have -
- Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is -
- Let y^2 = 12x be the parabola with its vertex at O. Let P be a point on the parabola and A be a point on the x-axis such that OPA...
- Let the line L pass through the point (-3, 5, 2) and make equal angles with the positive coordinate axes. If the distance of L...
- If the image of the point P(1, 2, a) in the line x-6 3 = y-7 2 = 7-z 2 is Q(5, b, c), then a^2 + b^2 + c^2 is equal to
- Let L be the line x+1 2 = y+1 3 = z+3 6 and let S be the set of all points (a,b,c) on L, whose distance from the line x+1 2 = y+1...
- The vertices B and C of a triangle ABC lie on the line x 1 = 1-y -2 = z-2 3 . The coordinates of A and B are (1,6,3) and (4,9, )...
- Let the direction cosines of two lines satisfy the equations: 4 +m-n=0 and 2mn+10n +3 m=0. Then the cosine of the acute angle...
- Let the lines L_1: r = i +2 j +3 k + (2 i +3 j +4 k ), R and L_2: r = (4 i + j )+ (5 i +2 j + k ), R , intersect at the point R....
- Let a line L passing through the point P(1,1,1) be perpendicular to the lines x-4 4 = y-1 1 = z-1 1 and x-17 1 = y-71 1 = z 0 ....
- If the distances of the point (1,2,a) from the line x-1 1 = y 2 = z-1 1 along the lines L_1: x-1 3 = y-2 4 = z-a b and L_2: x-1 1...
- If the distance of the point P(43, , ), <0, from the line r =4 i - k + (2 i +3 k ), R along a line with direction ratios 3,-1,0...
- Let L1 : x-1 3 = y-1 -1 = z+1 0 and L2 : x-2 2 = y 0 = z+4 , α ∈R, be two lines, which intersect at the point B. If P is the foot...
- The distance of the line x-2 2 = y-6 3 = z-3 4 from the point (1, 4, 0) along the line x 1 = y-2 2 = z+3 3 is :
- Let in a ABC, the length of the side AC be 6, the vertex B be (1, 2, 3) and the vertices A, C lie on the line x-6 3 = y-7 2 = z-7...
- Let the line passing through the points (–1, 2, 1) and parallel to the line x-1 2 = y+1 3 = z 4 intersect the line x+2 3 = y-3 2...
- Let a = 3 i - j +2 k , b = a ( i -2 k ) and c = b k . Then the projection of c -2 j on a is :
- Let P be the image of the point Q(7, -2, 5) in the line L : x-1 2 = y+1 3 = z 4 and R(5, p, q) be a point on L. Then the square...
- Let A(x, y, z) be a point in xy-plane, which is equidistant from three points (0, 3, 2), (2, 0, 3) and (0, 0, 1). Let B = (1, 4,...
Page 1Next
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