1
In a three-dimensional xyz space, the equation x² - 5x + 6 = 0 represe ...
Three Dimensional Geometry
2
For the line (x - 1) /1=( y - 2)/2 =( z - 3)/3, which one of the follo ...
Three Dimensional Geometry
3
The intercept made by the plane r · n = q on the x-axis is ...
Three Dimensional Geometry
4
Let A (a) and B (b) be points on two skew lines r = a + λp and r = b + ...
Three Dimensional Geometry
5
The point on the line (x-2)/1 = (y+3)/-2 = (z+5)/-2 at a distance of 6 ...
Three Dimensional Geometry
6
If P₁: r · n₁ - d₁ = 0, P₂: r · n₂ - d₂ = 0 and P₃: r · n₃ - d₃ = 0 ar ...
Three Dimensional Geometry
7
Line r = a + λb will not meet the plane r · n = q, if ...
Three Dimensional Geometry
8
If a line makes an angle of π/4 with the positive direction of each of ...
Three Dimensional Geometry
9
The ratio in which the plane r · (i - 2j + 3k) = 17 divides the line j ...
Three Dimensional Geometry
10
The length of the perpendicular drawn from (1, 2, 3) to the line (x-6) ...
Three Dimensional Geometry
11
The intersection of the spheres x² + y² + z² + 7x - 2y - z = 13 and x² ...
Three Dimensional Geometry
12
A line makes an angle θ with each of the x- and z-axes. If the angle β ...
Three Dimensional Geometry
13
The centre of the circle given by r · (i + 2j + 2k) = 15 and |r - (j + ...
Three Dimensional Geometry
14
The lines which intersect the skew lines y = mx, z = c; y = -mx, z = - ...
Three Dimensional Geometry
15
If( X-2)/3 =( y + 1)/2 =z- 1 /-1intersects the curve xy = c, z = 1, th ...
Three Dimensional Geometry
16
If the foot of the perpendicular from the origin to a plane is P (a, b ...
Three Dimensional Geometry
17
The coordinates of the foot of the perpendicular drawn from the origin ...
Three Dimensional Geometry
18
The point of intersection of the line passing through (0, 0, 1) and in ...
Three Dimensional Geometry
19
Distance of point P (p) from the plane r · n = 0 is ...
Three Dimensional Geometry
20
The reflection of the point a in the plane r · n = q is ...
Three Dimensional Geometry
21
If angle θ between the line (x+1)/1 = (y-1)/2 = (z-2)/1 and the plane ...
Three Dimensional Geometry
22
The radius of the circle in which the sphere x² + y² + z² + 2x - 2y - ...
Three Dimensional Geometry
23
Two systems of rectangular axes have the same origin. If a plane cuts ...
Three Dimensional Geometry
24
The plane r · n = q will contain the line r = a + λb, if ...
Three Dimensional Geometry
25
The Cartesian equation of the plane r = (1 + λ - μ)i + (2 - λ)j + (3 - ...
Three Dimensional Geometry
26
The value of m for which straight line 3x - 2y + z + 3 = 0 = 4x - 3y + ...
Three Dimensional Geometry
27
Equation of a line in the plane π = 2x - y + z - 4 = 0 which is perpen ...
Three Dimensional Geometry
28
The equation of a plane which passes through the point of intersection ...
Three Dimensional Geometry
29
Let A (1, 1, 1), B (2, 3, 5) and C (-1, 0, 2) be three points, then eq ...
Three Dimensional Geometry
30
The length of projection of the line segment joining the points (1, 0, ...
Three Dimensional Geometry
31
Shortest distance between the lines (x-1)/1 = (y-1)/1 = (z-1)/1 and (x ...
Three Dimensional Geometry
32
The distance between the line r = 2i - 2j + 3k + λ(i - j + 4k) and the ...
Three Dimensional Geometry
33
Let L be the line of intersection of the planes 2x + 3y + z = 1 and x ...
Three Dimensional Geometry
34
A tetrahedron has vertices O (0, 0, 0), A (1, 2, 1), B (2, 1, 3) and C ...
Three Dimensional Geometry
35
The point of intersection of the lines (x-5)/3 = (y-7)/-1 = (z+2)/1 an ...
Three Dimensional Geometry
36
The plane which passes through the point (3, 2, 0) and the line (x-3)/ ...
Three Dimensional Geometry
37
The direction ratios of a normal to the plane through (1, 0, 0) and (0 ...
Three Dimensional Geometry
38
From the point P(a, b, c), let perpendiculars PL and PM be drawn to YO ...
Three Dimensional Geometry
39
Let the equations of a line and a plane be x + 3/2 = y - 4/3 = z + 5/2 ...
Three Dimensional Geometry
40
The distance of point A (-2, 3, 1) from the line PQ through P (-3, 5, ...
Three Dimensional Geometry
41
A unit vector parallel to the intersection of the planes r · (i + j + ...
Three Dimensional Geometry
42
Let L1 be the line r1 = 2i + j - k + λ (i + 2k) and let L2 be the line ...
Three Dimensional Geometry
43
If lines x = y = z and x = y/2 = z/3 and third line passing through (1 ...
Three Dimensional Geometry
44
The image of the point (-1, 3, 4) in the plane x - 2y = 0 is ...
Three Dimensional Geometry
45
The shortest distance from the plane 12x + y + 3z = 327 to the sphere ...
Three Dimensional Geometry
46
The lines (x-2)/1 = (y-3)/1 = (z-4)/-1 and (x-3)/1 = (y-4)/1 = (z-5)/1 ...
Three Dimensional Geometry
47
Distance of the point P (p) from the line r = a + λb is ...
Three Dimensional Geometry
