MCQs of Three Dimensional Geometry

Three Dimensional Geometry MCQs

MCQs of Three Dimensional Geometry

Showing 31 to 40 out of 188 Questions

31.

If \frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{4} and \frac{x - 3}{1} = \frac{y - k}{2} = \frac{z}{1} are intersecting lines then k =

(a)	$\frac{3}{2}$
(b)	$\frac{9}{2}$
(c)	$\frac{- 2}{9}$
(d)	$\frac{- 3}{2}$

32.

Angle between the two diagonals of cube is _____

(a)	45°
(b)	60°
(c)	30°
(d)	$\tan^{- 1} (2, \sqrt{2})$

33.

The two lines x = ay + b, z = cy + d and x = a' y + b', z = c' y + d will be perpendicular, if and only if

(a)	aa' + bb' + cc' = 0
(b)	(a + a')+(b + b')+(c +c') = 0
(c)	aa' + cc' + 1 = 0
(d)	aa' + bb' + cc' + 1 = 0

34.

The lines \frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{- k} and \frac{x - 1}{k} = \frac{y - 4}{2} = \frac{z - 5}{1} are coplanar if

(a)	k = 1 or -1
(b)	k = 0 or -3
(c)	k = 3 or -3
(d)	k = 0 or -1

35.

A tetrahedron has vertices at O(0,0,0), A(1,2,1), B(2,1,3) and C(-1,1,2). Then the angle between the faces OAB and ABC will be

(a)	$\cos^{- 1} (\frac{19}{35})$
(b)	$\cos^{- 1} (\frac{17}{31})$
(c)	30°
(d)	90°

36.

Two system of retangular axes have the same origin. If a plane cuts them at distances a, b, c and a', b', c' from the origin then.

(a)	$\frac{1}{a^{2}} + \frac{1}{b^{2}} + \frac{1}{c^{2}} - \frac{1}{a'^{2}} - \frac{1}{b'^{2}} - \frac{1}{c'^{2}} = 0$
(b)	$\frac{1}{a^{2}} + \frac{1}{b^{2}} + \frac{1}{c^{2}} + \frac{1}{a'^{2}} + \frac{1}{b'^{2}} + \frac{1}{c'^{2}} = 0$
(c)	$\frac{1}{a^{2}} + \frac{1}{b^{2}} + \frac{1}{c^{2}} + \frac{1}{a'^{2}} + \frac{1}{b'^{2}} - \frac{1}{c'^{2}} = 0$
(d)	$\frac{1}{a^{2}} - \frac{1}{b^{2}} - \frac{1}{c^{2}} + \frac{1}{a'^{2}} - \frac{1}{b'^{2}} - \frac{1}{c'^{2}} = 0$

37.

A line with direction cosines proportional to 2,1,2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the points of intersection are given by

(a)	(3a, 2a, 3a), (a, a, 2a)
(b)	(3a, 2a, 3a), (a, a, a)
(c)	(3a, 3a, 3a), (a, a, a)
(d)	(2a, 3a, 3a), (2a, a, a)

38.

The image of the point (-1,3,4) in the plane x - 2y = 0 is

(a)	$(\frac{- 17}{3}, \frac{- 19}{3}, 4)$
(b)	$(\frac{- 17}{3}, \frac{- 19}{3}, 1)$
(c)	(15,11,4)
(d)	$(\frac{9}{5}, \frac{- 13}{5}, 4)$

39.

If a line makes an angle of

\frac{π}{4}

with the positive directions of each of X - axis and Y - axis, then the angle that the line makes with the positive direction of the Z - axis is

(a)	$\frac{π}{4}$
(b)	$\frac{π}{2}$
(c)	$\frac{π}{6}$
(d)	$\frac{π}{3}$

40.

The line passing through the points (5,1,a) and (3,b,1) crosses the yz - plane at the point.

(0, \frac{17}{2}, \frac{- 13}{2})

. Then

(a)	a = 8, b = 2
(b)	a =2, b = 6
(c)	a =4, b = 6
(d)	a = 6, b = 4

Showing 31 to 40 out of 188 Questions