Three Dimensional Geometry questions
879 published questions with worked solutions.
- Let the foot of perpendicular of the point P(3, –2, –9) on the plane passing through the points (–1, –2, –3), (9, 3, 4), (9, –2,...
- If the line x = y = z intersects the line xsinA + ysinB + zsinC – 18 = 0 = xsin2A + ysin2B + zsin2C – 9, where A, B, C are the...
- Let the plane P contain the line 2x + y – z – 3 = 0 = 5x – 3y + 4z + 9 and be parallel to the line x+2 2 = 3-y -4 = z-7 5 . Then...
- Let the plane containing the line of intersection of the planes P_1: x + ( +4)y + z = 1 and P_2 : 2x + y + z = 2 pass through the...
- If the foot of the perpendicular drawn from the point (1, 9, 7) to the line passing through the point (3, 2, 1) and parallel to...
- The distance of a point (7, –3, –4) from the plane passing through the points (2, –3, 1), (–1, 1, –2) and (3, –4, 2) is
- Let A(–1, 1, 1) C(1, –1, 1) and D(2, –1, 2 ) be four distinct points on a plane. If the direction ratios of the lines AC and AD...
- The foot of perpendicular of the point (2, 0, 5) on x+1 2 = y-1 5 = z+1 -1 is ( , , ). Then, which of the following is NOT...
- The foot of perpendicular of the point (2, 0, 5) on x+1 2 = y-1 5 = z+1 -1 is ( , , ). Then, which of the following is NOT...
- Consider the lines L_1 and L_2 given by L_1 : x-1 2 = y-3 1 = z-2 2 , L_2 : x-2 1 = y-2 2 = z-3 3 A line L_3 having direction...
- The distance of the point P(4. 6, –2) from the line passing through the point (–3, 2, 3) and parallel to a line with direction...
- Let the equation of the plane passing through the line x – 2y – z – 5 = 0 = x + y + 3z – 5 and parallel to the line x + y + 2z –...
- If the lines x-1 1 = y-2 2 = z+3 1 and x-a 2 = y+2 3 = z-3 1 intersect at the point P, then the distance of the point P from the...
- Let the equation of the plane P containing the line x + 10 = 8-y 2 = z be ax + by + 3z = 2(a + b) and the distance of the plane P...
- Let the co-ordinates of one vertex of be A(0, 2, ) and the other two vertices lie on the line x+ 5 = y-1 2 = z+4 3 . For Z, if...
- If a plane passes through the points (–1, k, 0), (2, k, –1), (1, 1, 2) and is parallel to the line x-1 1 = 2y+1 2 = z+1 -1 , then...
- A vector v in the first octant is inclined to the x-axis at 60°, to the y-axis at 45° and to the z-axis at an acute angle. If a...
- Let a line L pass through the point P(2, 3, 1) and be parallel to the line x + 3y – 2z – 2 = 0 = x – y + 2z. If the distance of L...
- Let a unit vector OP makes angles , , with the positive directions of the co-ordinate axes OX, OY, OZ respectively, where (0, 2...
- If the equation of the plane passing through the point (1, 1, 2) and perpendicular to the line x – 3y + 2z – 1 = 0 = 4x – y + z...
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