Question

30. The point of intersection of the lines
represented by i =(i + 2j-k) + 2(21
+ 3j + 4k) and i = (-i - 3] + 7k) +
u(i + 2; - k) is
(1) 3i+57 + 3k
(2) 57 +81 +7
(3) - 1 - 1 -5k
(4) - 31 – 4) - 92


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Answer 1

Answer:

Let the lines are M:r=3i+2j−4k+λ(i+2j+2k) and N:r=5i−2j+μ(3i+2j+6k)

Coordinates of any random point on M are P(3+λ,2+2λ,−4+2λ) and on N are Q(5+3μ,−2+2μ,6μ)

If the lines M and N intersect then, they must have a common point on them i.e., P and Q must coincide for some values of λ and μ

Now, 3+λ=5+3μ ----- (1)

2+2λ=−2+2μ----- (2

−4+2λ=6μ-----(3)

Solving 1 and 2, 

we get λ=−4,μ=−2

Substitute the values in equation 3,

−4+2(−4)=6(−2)

−4=−12+8

−4=−4

So, the given lines intersect each other

Now, point of intersection is P(−1,−6,−12).