Page 88 - Mathematics Class - XII

Viva-Voce

1. What are skew lines?
Ans. Skew lines are lines in space which are neither parallel nor intersecting. They lie in different planes.
2. Can two skew lines exist in same plane?
Ans. No, two skew lines can’t exist in same plane. They lie in different planes.

3. Define the vector formula for finding shortest distance between two skew lines.

Ans. Let vector equations of two skew lines be r a b and r a b ,
1
2
2
1

(a a )
) (bb
then shortest distance between them = 2 1 2
1
bb

1 2
4. What is the formula for shortest distance between two parallel lines?

b
Ans. Let vector equations of two parallel lines be r a b and r a ,
1 2

(a a ) b
then shortest distance between them = 2 1
b
5. What is the condition of coplanarity of two lines?

Ans. Two lines r a and r a b are coplanar if (a a ) (bb ) = 0
1 b1 2 2 2 1 1 2

MCQs

1. Distance between the two planes: 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is

2
a) 2 units b) 4 units c) 8 units d) units
29
2. The planes: 2 – y + 4z = 5 and 5 – 2.5 y + 10z = 6 are

a) Perpendicular b) Parallel c) Intersect y-axis d) Passes through 00,, 5

4
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
a) cos 1 b) cos c) cos d) cos
1
1
15 15 8 8

k) and
k )
4. The shortest distance between the lines whose vector equations are r ( i 2 j 3 ( i 3 j 2

r 4 i 5 j 6 k ( 2 i 3 j 4 k)
a) 3 b) 6 c) 1 d) None of these
19 19 19
2 8 3
Answers: 1. d) units 2. b) Parallel 3. b) cos 4. a)
1
29 15 19
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