UP Board Class 12 Three Dimensional Geometry — practice questions
34 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice UP Board Class 12 Three Dimensional Geometry in the app →The distance between $(1, 2, 3)$ and $(4, 6, 3)$ in 3D is:The direction cosines of a line with direction ratios $(2, -1, 2)$ are:The plane $2x - y + 3z + 5 = 0$ has normal vector:The distance from $(1, 1, 1)$ to the plane $2x + 2y + z + 3 = 0$ is:If l, m, n are the direction cosines of a line in space, thenThe vector equation of a line passing through point a and parallel to vector b isThe equation of a plane in normal form (with unit normal n̂ and perpendicular distance d from origin) isA plane meets the axes at (a,0,0), (0,b,0), (0,0,c). Its equation isThe direction cosines of the line joining (1, 2, 3) and (4, 5, 6) areThe Cartesian equation (x-1)/2 = (y-2)/3 = (z-3)/4 representsThe angle θ between two lines with direction vectors b₁ and b₂ is given byThe distance of the point (x₀, y₀, z₀) from the plane ax + by + cz + d = 0 isThe shortest distance between skew lines r = a₁ + λb₁ and r = a₂ + μb₂ isTwo lines r = a₁ + λb₁ and r = a₂ + μb₂ are coplanar if and only ifThe angle between two planes with normals n₁ and n₂ is given byThe angle ϕ between a line with direction b and a plane with normal n satisfiesThe equation of a plane passing through point (x₁, y₁, z₁) with normal vector (a, b, c) isTwo lines with direction vectors b₁ and b₂ are parallel if and only ifThe equation of a plane through the intersection of π₁ = 0 and π₂ = 0 has the formThe perpendicular distance from a point P with position vector p to a line r = a + λb isFor two skew lines (x-x₁)/a₁ = (y-y₁)/b₁ = (z-z₁)/c₁ and (x-x₂)/a₂ = (y-y₂)/b₂ = (z-z₂)/c₂, the shortest distaThe angle between the lines with direction ratios (1, 2, 2) and (2, 1, 2) satisfiesThe distance of the point (2, 1, -1) from the plane 2x - y + 2z + 5 = 0 isThe angle between the planes 2x - y + 2z = 5 and x + 2y - 2z = 4 satisfiesThe equation of the plane through the points (1,0,0), (0,1,0), (0,0,1) isThe distance between the parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z = 5 isThe line r = (2, -1, 4) + λ(3, 0, 2), expressed in symmetric Cartesian form, isThe shortest distance between r = (1,2,3) + λ(2,3,4) and r = (2,4,5) + μ(3,4,5) isThe equation of a plane parallel to x + 2y - 3z = 5 and passing through (1, 1, 1) isThe plane through the points (1,1,0), (1,0,1) and (0,1,1) has equationA line has direction ratios (1, 1, 2) and meets the plane x - y + z = 0. The angle ϕ between them satisfiesThe line through the origin with direction ratios (1, 1, 1) meets the plane x + y + z = 6 atThe foot of the perpendicular from origin to the plane 2x + 3y - 6z = 14 isThe image of the point (1, 2, 3) in the plane x + y + z = 0 is