Three Dimensional Geometry questions
879 published questions with worked solutions.
- Let ( , 2, 1) be a point on the plane which passes through the point (4, –2, 2). If the plane is perpendicular to the line...
- Let a line having direction ratios 1, −4, 2 intersect the lines (x − 7)/3 = (y − 1)/−1 = (z + 2)/1 and x/2 = (y − 7)/3 = z/1 at...
- Let the points on the plane P be equidistant from the points (−4, 2, 1) and (2, −2, 3). Then the acute angle between the plane P...
- The centroid of the triangle whose three sides are given by the combined equation (x^2+7xy+2y^2 )(y-1)=0, is
- A plane E is perpendicular to the two planes 2x − 2y + z = 0 and x − y + 2z = 4, and passes through the point P(1, −1, 1). If the...
- Let P be the plane containing the straight line (x − 3)/9 = (y + 4)/(−1) = (z − 7)/(−5) and perpendicular of the plane containing...
- Let P be the plane passing through the intersection of the planes r ( i + 3 j - k ) = 5 and r (2 i - j + k ) = 3, and the point...
- Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S : x + y + z = 5. If a line L passing through (1,...
- Let x = 2t, y = t^ 2 /3 be a conic. Let S be the focus and B be the point on the axis of the conic such that SA BA, where A is...
- Let the lines L_ 1 : r = ( i + 2 j + 3 k ), ℝ and L_ 2 : r = ( i + 3 j + k ) + ( i + j + 5 k ), ℝ intersect at the point S. If a...
- The plane passing through the line L : x - y + 3(1 - )z = 1, x + 2y − z = 2 and perpendicular to the plane 3x + 2y + z = 6 is 3x...
- The length of the perpendicular from the point (1, −2, 5) on the line passing through (1, 2, 4) and parallel to the line x + y −...
- Let Q and R be two points on the line (x + 1)/2 = (y + 2)/3 = (z − 1)/2 at a distance 26 from the point P(4, 2, 7). Then the...
- If the plane 2x + y − 5z = 0 is rotated about its line of intersection with the plane 3x − y + 4z − 7 = 0 by an angle of /2, then...
- Let the plane 2x + 3y + z + 20 = 0 be rotated through a right angle about its line of intersection with the plane x − 3y + 5z =...
- The distance of the point (–1, 2, –2) from the line of intersection of the planes 2x + 3y + 2z = 0 and x – 2y + z = 0 is :
- Suppose the line x-2 = y-2 -5 = z+2 2 lies on the plane x + 3y – 2z + = 0. Then ( + ) is equal to_____.
- Let the plane P pass through the intersection of the planes 2x + 3y – z = 2 and x + 2y + 3z = 6, and be perpendicular to the...
- The point of intersection C of the plane 8x + y + 2z = 0 and the line joining the points A(–3, –6, 1) and B(2, 4, –3) divides the...
- Let + + = 1 be the equation of a plane passing through the point (3, –2, 5) and perpendicular to the line joining the points (1,...
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