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Show that the line (x-1)/2=(y-2)/3=(z-3...

Show that the line `(x-1)/2=(y-2)/3=(z-3)/4a n d(x-4)/5=(y-1)/2` intersect. Find their point of intersection.

A

(0,0,0)

B

(1,1,1)

C

(-1,-,1,-1)

D

(1,2,3)

Text Solution

Verified by Experts

The correct Answer is:
C
Given lines are `(x-1)/(2)=(y-2)/(3)=(z-3)/(4)=r["say"]......(i)`
`and (x-4)/(5)=(y-1)/(2)=z.....(ii)`
Any point on the line (i) is (2r+1, 3r+2, 4r+3)
If they interest, then the point satisfies the second line we get `(2r+1-4)/(5)=(3r+2-1)/(2)=4r+3`
`Rightarrow (2r-3)/(5)=(3r-1)/(2) Rightarrow r=-1`
`therefore` Required point is [(2(-1)+1,3(-1)+2,4(-1)+3]
`=(-2+1,-3+2,-4+3)`
=(-1,-1,-1)
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