Page 89 - Mathematics Class - XII

Case-Study Based Questions
Case-Study Based Questions
If a , b , c and a , b , c are direction ratios of two lines say L and L respectively. L 1 L
1
2
2
2
1
2
1
1
a b c 2
Then L || L iff 1 1 1 andL L iff a a + b b + c c = 0.
1 2 a b c 1 2 1 2 1 2 1 2 L 1
2 2 2
Based upon the above information, answer the following questions L 2
1. If l , m , n and l , m , n are the direction cosines of L and L
1
1
2
1
2
1
2
2
respectively. Then L will be perpendicular to L iff
1 2
(a) l l + m m + n n = 0 (b) l 1 = m 1 = n 1 (c) l m + m l + n n = 0 (d) None of these
1 2
1 2
1 2
l 2 m 2 n 2 1 2 1 2 1 2
2. If l , m , n and l , m , n are the direction cosines of L and L respectively. Then L will be perpendicular
2
1
1
2
2
1
1
2
1
to L iff
2
(a) l l + m m + n n = 0 (b) l m + m l + n n = 0
1 2 1 2 1 2 1 2 1 2 1 2
l m n
(c) 1 = 1 = 1 (d) m n + m n + l l = 0
l m n 1 2 2 1 1 2
2 2 2
3. The coordinates of the foot of the perpendicular drawn from the point A (1, 2, 1) to the line joining
B (1, 4, 6) and C (5, 4, 4) are
(a) (1, 2, 1) (b) (2, 4, 5) (c) (3, 4, 5) (d) (4, 3, 5)
4. The lines x 2 y 1 z 2 and x 1 y 32(/ ) z 5 are
3 2 0 1 (/ 2
32)
(a) Parallel (b) Perpendicular (c) Skew lines (d) Non-intersecting
Assertion-Reason Based Questions
Assertion-Reason Based Questions
Directions for Questions 1 to 2: In each of the questions given below, there are two statements marked as
Assertion (A) and Reason (R). Mark your answer as per the codes provided below:
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false. (d) A is false but R is true.

k)
Q. 1. Assertion (A) : If a is an integer, then the straight lines r ( i 2 j 3 k ) ( ai 2 j 3 and

r 2 i 3 jk ( 3 ia j
k 2 ) intersect at a point for a = –5.
Reason (R) : Two straight lines intersect if the shortest distance between them is zero.
x y z x 1 y 1 z 1
Q. 2. Assertion (A) : The shortest distance between the lines and is 2 .
2 1 2 4 2 4
Reason (R) : The shortest distance between two parallel lines is the perpendicular distance from
any point on one of the lines to the other lines.
Answers
Case-Study Based Questions: 1. (a) 2. (c) 3. (c) 4. (b)
Assertion-Reason Based Questions: 1. (a) 2. (a)

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