1
In a three-dimensional xyz space, the equation x² - 5x + 6 = 0 represents ...
2
For the line (x - 1) /1=( y - 2)/2 =( z - 3)/3, which one of the following is incorrect? ...
3
The intercept made by the plane r · n = q on the x-axis is ...
4
Let A (a) and B (b) be points on two skew lines r = a + λp and r = b + μq and the shortest distance ...
5
The point on the line (x-2)/1 = (y+3)/-2 = (z+5)/-2 at a distance of 6 from the point (2, -3, -5) is ...
6
If P₁: r · n₁ - d₁ = 0, P₂: r · n₂ - d₂ = 0 and P₃: r · n₃ - d₃ = 0 are three planes and n₁, n₂, and ...
7
Line r = a + λb will not meet the plane r · n = q, if ...
8
If a line makes an angle of π/4 with the positive direction of each of x-axis and y-axis, then the a ...
9
The ratio in which the plane r · (i - 2j + 3k) = 17 divides the line joining the points -2i + 4j + 7 ...
10
The length of the perpendicular drawn from (1, 2, 3) to the line (x-6)/3 = (y-7)/2 = (z-1)/-2 is ...
11
The intersection of the spheres x² + y² + z² + 7x - 2y - z = 13 and x² + y² + z² - 3x + 3y + 4z = 8 ...
12
A line makes an angle θ with each of the x- and z-axes. If the angle β, which it makes with the y-ax ...
13
The centre of the circle given by r · (i + 2j + 2k) = 15 and |r - (j + 2k)| = 4 is ...
14
The lines which intersect the skew lines y = mx, z = c; y = -mx, z = -c and the x-axis lie on the su ...
15
If( X-2)/3 =( y + 1)/2 =z- 1 /-1intersects the curve xy = c, z = 1, then c is equal to ...
16
If the foot of the perpendicular from the origin to a plane is P (a, b, c), the equation of the plan ...
17
The coordinates of the foot of the perpendicular drawn from the origin to the line joining the point ...
18
The point of intersection of the line passing through (0, 0, 1) and intersecting the lines x + 2y + ...
19
Distance of point P (p) from the plane r · n = 0 is ...
20
The reflection of the point a in the plane r · n = q is ...
21
If angle θ between the line (x+1)/1 = (y-1)/2 = (z-2)/1 and the plane 2x - y + λz + 4 = 0 is such th ...
22
The radius of the circle in which the sphere x² + y² + z² + 2x - 2y - 4z - 19 = 0 is cut by the plan ...
23
Two systems of rectangular axes have the same origin. If a plane cuts them at distance a, b, c and a ...
24
The plane r · n = q will contain the line r = a + λb, if ...
25
The Cartesian equation of the plane r = (1 + λ - μ)i + (2 - λ)j + (3 - 2λ + 2μ)k is ...
26
The value of m for which straight line 3x - 2y + z + 3 = 0 = 4x - 3y + 4z + 1 is parallel to the pla ...
27
Equation of a line in the plane π = 2x - y + z - 4 = 0 which is perpendicular to the line l whose eq ...
28
The equation of a plane which passes through the point of intersection of lines (x-1)/3 = (y-2)/1 = ...
29
Let A (1, 1, 1), B (2, 3, 5) and C (-1, 0, 2) be three points, then equation of a plane parallel to ...
30
The length of projection of the line segment joining the points (1, 0, -1) and (-1, 2, 2) on the pla ...
31
Shortest distance between the lines (x-1)/1 = (y-1)/1 = (z-1)/1 and (x-2)/1 = (y-3)/1 = (z-4)/1 is e ...
32
The distance between the line r = 2i - 2j + 3k + λ(i - j + 4k) and the plane r · (i + 5j + k) = 5 is ...
33
Let L be the line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2z = 2. If L makes an a ...
34
A tetrahedron has vertices O (0, 0, 0), A (1, 2, 1), B (2, 1, 3) and C (-1, 1, 2), then angle betwee ...
35
The point of intersection of the lines (x-5)/3 = (y-7)/-1 = (z+2)/1 and (x+3)/-36 = (y-3)/2 = (z-6)/ ...
36
The plane which passes through the point (3, 2, 0) and the line (x-3)/1 = (y-6)/5 = (z-4)/4 is ...
37
The direction ratios of a normal to the plane through (1, 0, 0) and (0, 1, 0), which makes an angle ...
38
From the point P(a, b, c), let perpendiculars PL and PM be drawn to YOZ and ZOX planes, respectively ...
39
Let the equations of a line and a plane be x + 3/2 = y - 4/3 = z + 5/2 and 4x - 2y - z = 1, respecti ...
40
The distance of point A (-2, 3, 1) from the line PQ through P (-3, 5, 2), which makes equal angles w ...
41
A unit vector parallel to the intersection of the planes r · (i + j + k) = 5 and r · (2i + j - 3k) = ...
42
Let L1 be the line r1 = 2i + j - k + λ (i + 2k) and let L2 be the line r2 = 3i + j + μ (i + j - k). ...
43
If lines x = y = z and x = y/2 = z/3 and third line passing through (1, 1, 1) form a triangle of are ...
44
The image of the point (-1, 3, 4) in the plane x - 2y = 0 is ...
45
The shortest distance from the plane 12x + y + 3z = 327 to the sphere x² + y² + z² + 4x - 2y - 6z = ...
46
The lines (x-2)/1 = (y-3)/1 = (z-4)/-1 and (x-3)/1 = (y-4)/1 = (z-5)/1 are coplanar if ...
47
Distance of the point P (p) from the line r = a + λb is ...
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