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