# Multiple choice (3 Dimensional Geometry)

`Â  Choose and write the correct option in the following question:(Multiple choice question of 3 dimensional geometry)

1.) The co-ordinates of the foot of the perpendicular drawn from the point (2, -3, 4) on the y-axis is

(a) (2, 3, 4)Â  Â  Â  Â  Â  Â  Â  Â  Â (b) (-2, -3, -4)

(c) (0, -3, 0)Â  Â  Â  Â  Â  Â  Â  Â  (d) (2, 0, 4)

2.) If a lines makes angles Î±, Î² and Î³ with the axis respectively, then

(a) -2Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b) -1

(c) 1Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (d) 2

3.) Distance of the point (Î±, Î², Î³) from y-axis is

(a) Î²Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b) |Î²|

(c) |Î²|+|Î³|Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (d) âˆš(Î±Â²+Î³Â²)

4.) If the direction cosines of a line are k, k, k then

(a) k > 0Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) 0 < k < 0

(c) k = 1Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (d) or

5.) The angle between the two diagonals of a cube is

(a) 30Â°Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) 45Â°

(c) Â  Â (d)

6.) If a line makes angles Î±, Î², Î³, Î´ with four diagonals of a cube, then

is equal to

(a) 1/3Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b) 2/3

(c) 4/3Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) 8/3

7.) If a line makes angle Ï€/3 and Ï€/4 with x-axis and y-axis respectively,then the angle made by the line with z-axis is

(a) Ï€/2Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b) Ï€/3

(c) Ï€/4Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (d) 15Ï€/12

8.) P is a point on the line segment joining the points (3, 2, -1) and (6, 2, -2). If x-coordinate of P is 5, then its y co-ordinate is

(a) 2Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) 1

(c) -1Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (d)Â  -2

9.) If Î±, Î², Î³ are the angles that a line makes with the positive direction of x, y, z axis, respectively. then the direction cosines of the line are

(a)

(b)

(c)

(d)

10.) The distance of a point P(a, b, c) from x-axis is

(a) Â  Â  Â  Â (b)

(c) Â  Â  Â  Â (d)

11.) The equation of x-axis in space are

(a) x = 0, y = 0Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) x = 0, y = 0

(c) x = 0Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) y = 0, z = 0

12.) A line makes equal angles with co-ordinate axis. Direction cosine of this line are

(a) Â±(1, 1, 1)Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) Â±(1/âˆš3, 1/âˆš3, 1/âˆš3)

(c) Â±(1/3, 1/3, 1/3)Â  Â  Â  Â  Â  Â (d)Â  Â±(1/âˆš3, -1/âˆš3, -1/âˆš3)

13.) The distance of the point (1, 6, 3) to the line is

(a) âˆš13Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) 13

(c) 2âˆš13Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) None of these

14.) The two lines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ will be perpendicular, if and only ifÂ

(a) aa’ + cc’ + 1 = 0Â  Â  Â  Â  Â  (b) aa’ + bb’ + cc’ + 1 = 0

(c) aa’ + bb’ + cc’ =0Â  Â  Â  Â (d) (a + a’)(b + b’)(c + c’) = 0

15.) The area of the quadrilateral ABCD where A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2) is equal to

(a) 9 sq.unitsÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) 18 sq.units

(c) 27 sq.unitsÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) 81 sq.units

16.) The straight line is

(a) Parallel to x-axisÂ  Â  Â  Â  Â (b) Parallel to y-axis

(c) Parallel to z-axisÂ  Â  Â  Â  Â  Â (d) Perpendicular to z-axis

17.) The shortest distance between the lines given by and is

(a) 7 unitsÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) 2 units

(c) 14 unitsÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) 3 units

18.) The image of the point (1, 6, 3) in the line is

(a) (2, 0, 5)Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b) (1, 3, 4)

(c) (1, 0, 7)Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (d) (-3, -2, 0)

19.) The shortest distance between the line and the y -axis is

(a) 1/5Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b) 1

(c) 0Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (d) 12/5

20.) The co-ordinates of the foot of perpendicular drawn from point A (1, 8, 4) to the line joining the points B(0, -1, 3) and C (2, -3, -1) are

(a) (-7/3, 2/3, 11/3)Â  Â  Â  Â  Â  Â  Â (b) (-5/3, 2/3, 19/3)

(c) (4/3, 2/3, 11/3)Â  Â  Â  Â  Â  Â  Â  Â (d) None of these

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â