Question

The lines `(x - 1)/2 = (y + 1)/2 = (z - 1)/4` and `(x - 3)/1 = (y - k)/2 = z/1` intersect each other at point

पर्याय

• (–2, –4, 5)

• (–2, –4, –5)

• (2, 4, –5)

• (2, –5)

Answer 1

(–2, –4, –5)

Explanation:

Since, `(x - 1)/2 = (y + 1)/2 = (z - 1)/4` = λ  ...(i)

and `(x - 3)/1 = (y - 6)/2 = z/1`  ...(ii)

Now, any point on the line (i) is P(2λ + 1, 2λ – 1, 4λ + 1)

∴ `(2λ + 1 - 3)/1 = (2λ - 1 - 6)/2 = (4λ + 1)/1` ...[from (ii)]

So, 4λ – 4 = 2λ – 7

`\implies` 4λ – 2λ = –7 + 4 

`\implies` 2λ = –3

Hence, point of intersection P is

= `(2 xx (-3/2) + 1, 2 xx (-3/2) - 1, 4 xx (-3/2) + 1)`

= (–2, –4, –5)