Ncert Solutions Maths class 12th

m? = 6/-12 = -1/2
∴ Equation of AD is y-7 = 2 (x+1)
y = 2x+9
m? = 12/-6 = -2
∴ Equation of BE is y-1 = 1/2 (x+7)y
y = x/2 + 9/2
by (1) and (2)
2x+9 = (x+9)/2
=> 4x+18 = x+9
=> 3x = 9 => x=-3
∴ y=3

Total = 9 (10? )
Fav. Way =? C? (2? -2) +? C? (2? -1) = 36 (30) + 9 (15) = 1080 + 135
Probability = (36x30+9x15)/ (9x10? ) = (4x30+15)/10? = 135/10?

Sum obtained is a multiple of 4.
A = { (1,3), (2,2), (3,1), (2,6), (3,5), (4,4), (5,3) (6,2), (6,6)}
B: Score of 4 has appeared at least once.
B = { (1,4), (2,4), (3,4), (4,4), (5,4), (6,4), (4,1), (4,2), (4,3), (4,5), (4,6)}
Required probability = P (B/A) = P (B? A)/P (A)
= (1/36) / (9/36) = 1/9

Equation of
AB = r = (î + j) + λ (3j - 3k)
Let coordinates of M
= (1, (1 + 3λ), -3λ).
PM = -3î + (3λ - 1)j - 3 (λ + 1)k
AB = 3j - 3k
? PM ⊥ AB ⇒ PM · AB = 0
⇒ 3 (3λ - 1) + 9 (λ + 1) = 0
⇒ λ = -1/3

∴ M = (1,0,1)
Clearly M lies on 2x + y - z = 1.

r = î (1 + 12l) + j (-1) + k (l)
r = î (2 + m) + j (m - 1) + k (-m)
For intersection
1 + 2l = 2 + m
-1 = m - 1
l = -m
from (ii) m = 0
from (iii) l = 0
These values of m and l do not satisfy equation (1).
Hence the two lines do not intersect for any values of l and m.