Page 85 - Mathematics Class - XII

Viva-Voce

1. Define coordinates of a point in a space.
Ans. In order to locate the position of a point in a space, we require a rectangular coordinate system. After
choosing a fixed coordinate system in 3D, the coordinates of any point P in that system can be given by an
ordered 3-tuple (x, y, z). Also, if the coordinates (x, y, z) are already known then we can easily locate the
point P in space.
2. What is the distance formula between two points P(x , y , z ) and Q(x , y , z )?
2
2
1
1
1
2
Ans. Distance |PQ| = (x x ) (y y ) (z z ) 2
2
2
2 1 2 1 2 1
3. What is the locus of a point (x, y, z) for which x = 0, y = 0?
Ans. z-axis.
4. What is the coordinates of the foot of perpendicular from the point (x, y, z) on x-axis?
Ans. The coordinates of the foot of perpendicular from the point (x, y, z) on x-axis are (x, 0, 0) as on x-axis, y
and z coordinates of any point are zero.
5. If a plane is parallel to yz-plane, then it is perpendicular to which axis?
Ans. A plane parallel to yz-plane is perpendicular to x-axis.

MCQs

1. Which of the following is true.
a) l + m + n = 1 b) l – m – n = 0 c) l + m – n = 1 d) None of these
2
2
2
2
2
2
2
2
2
2. The distance from y-axis to point (α, β, γ) is
a) β b) | β | c) | β | + | γ | d) 2
2
3. The angle between the lines x 4 y 1 z 3 and x 1 y 4 z 5 is
3 5 4 1 1 2
83 8 1 3 15
1
a) cos 1 b) cos c) cos d) cos
1
15 15 8 8
1 x 7 y 14 z 3 77 x y 5 6 z
4. The value of λ, sothat the lines and are perpendicular, is
3 2 2 3 1 5
a) − 70 b) 70 c) 11 d) − 11
11 11 70 70
5. The distance between the points (2, 3) and (4, 1) is
a) 2 b) 1 c) 22 d) 52

6. The value of the acute angle between lines x – 2 = 0 and 3 xy 2 0 is

a) 0° b) 30° c) 45° d) 60°

1
Answers: 1. a) l + m + n = 1 2. d) 2 3. b) cos 8 4. b) 70 5. c) 22 6. b) 30°
2
2
2

2
15 11
83