Three Dimensional Geometry questions
879 published questions with worked solutions.
- If the angle between the lines, x 2 = y 2 = z 1 and 5 - x -2 = 7y - 14 p = z - 3 4 is ^ -1 ( 2 3 ), then p is equal to -
- The equation of a plane containing the line of intersection of the planes 2x - y - 4 = 0 and y + 2z - 4 = 0 and passing through...
- The length of the perpendicular from the point (2, −1, 4) on the straight line, x+3 10 = y-2 -7 = z 1 is:
- If a point R(4, y, z) lies on the line segment joining the points P(2, −3, 4) and Q(8, 0, 10), then the distance of R from the...
- The vector equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is...
- If the line, x-1 2 = y+1 3 = z-2 4 meets the plane, x + 2y + 3z = 15 at a point P, then the distance of P from the origin is:
- A plane passing through the points (0, −1, 0) and (0, 0, 1) and making an angle 4 with the plane y − z + 5 = 0, also passes...
- If the plane 2x - y + 2z + 3 = 0 has the distances 1 3 and 2 3 units from the planes 4x - 2y + 4z + = 0 and 2x - y + 2z + = 0,...
- A perpendicular is drawn from a point on the line x-1 2 = y+1 -1 = z 1 to the plane x + y + z = 3 such that the foot of the...
- A variable plane passes through a fixed point (3, 2, 1) and meets x, y and z axes at A, B and C respectively. A plane is drawn...
- An angle between the plane x + y + z = 5 and the line of intersection of the planes, 3x + 4y + z - 1 = 0 and 5x + 8y + 2z + 14 =...
- A plane bisects the line segment joining the points (1, 2, 3) and (–3, 4, 5) at right angles. Then this plane also passes through...
- An angle between the lines whose direction cosines are given by the equations, + 3m + 5n = 0 and 5 m - 2mn + 6n = 0, is -
- If a unit vector a makes angles π/3 with i, π/4 with j and θ ∈ (0, π) with k, then a value of θ is:
- Let P be the plane, which contains the line of intersection of the planes, x + y + z − 6 = 0 and 2x + 3y + z + 5 = 0 and it is...
- The vertices B and C of ΔABC lie on the line, x+2 3 = y-1 0 = z 4 such that BC = 5 units. Then the area (in sq. units) of this...
- If the length of the perpendicular from the point (β, 0, β) (β ≠ 0) to the line, x 1 = y-1 0 = z+1 -1 is 32 , then β is equal to:
- If Q(0, −1, −3) is the image of the point P in the plane 3x − y + 4z = 2 and R is the point (3, −1, −2), then the area (in sq....
- Let A(3, 0, −1), B(2, 10, 6) and C(1, 2, 1) be the vertices of a triangle and M be the midpoint of AC. If G divides BM in the...
- If the lines x = ay + b, z = cy + d and x = a′z + b′, y = c′z + d′ are perpendicular then:
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