THREE DIMENSIONAL GEOMETRY
- What is the equation of the plane
passing through the point (1, -1, -1) and
perpendicular to each of the planes x-
2y-8z= 0 and 2x+5y-z=0?
(a) 7x-3y+2z=14 (b) 2x+5y-3z=0 (c) x-
7y+3z=4 (d) 14x-5y+3z=16
- What is the angle between the planes
2x-y+z=4 and x+y+2z=6?
(a)^ (b)^ (c)^ (d)^
- What is the locus of points of
intersection of a sphere and a plane?
(a) Circle (b) Ellipse (c) Parabola (d)
Hyperbola
- The equation to sphere passing
through origin and the points (-1, 0, 0),
(0, -2, 0) and (0, 0, -3) is
( ). What is f(x, y, z) equal to?
(a) –x-2y-3z (b) x+2y+3z (c) x+2y+3z-
1 (d) x+2y+3z+1
- Let O(0, 0, 0), P(3, 4, 5), Q(m, n, r) and
R(1, 1, 1) be the vertices of a
parallelogram taken in order. What is
the value of m + n + r?
(a) 6 (b) 12 (c) 15 (d) More than 15
- In the line through the points A(k, 1, -
- and B(2k, 0, 2) is perpendicular to
the line through the points B and C
(2+2k, k, 1), then what is the value of k?
(a) -1 (b) 1 (c) -3 (d) 3
7. What is the value of n so that the
angle between the lines having
direction ratios (1, 1, 1) and (1, -1, n) is
60 ?
(a) √ (b) √ (c) 3 (d) None of these
8. A line makes the same angle α with
each of the x and y- axes. If the angle ,
which it makes with the z- axis, is such
that , then what is the
value of α?
(a)^ (b)^ (c)^ (d)^
9. What is the equation of the sphere
which has its centre at (6, -1, 2) and
touches the plane 2x-y+2z-2=0?
(a)
(b)
(c)
(d)
- Which one of the following planes is
normal to the plane 3x + y + z= 5?
(a) x + 2y + z= 6 (b) x – 2y + z= 6 (c) x
- 2y - z= 6 (d) x – 2y - z= 6
- If the radius of the sphere
is unity, what is the value of λ?
(a) 49 (b) 7 (c) -49 (d) - 7
- The straight line^ is
parallel to which one of the following?
(a) 4x + 3y – 5z= 0 (b) 4x + 5y – 4z= 0
(c) 4x + 4y – 5z= 0 (d) 5x + 4y – 5z= 0
