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Find the points on the line (x+2)/3=(y+1...

Find the points on the line `(x+2)/3=(y+1)/2=(z-3)/2\ ` at a distance of 5 units from the point `P(1,3,3,)dot`

Text Solution

Verified by Experts

The given line is
`(x+2)/(3)=(y+1)/(2)=(z-3)/(2)=r ` (say) …(i)

The general point of the this line is
`P(3r -2, 2r -1,2r+3)`
The given point is A(1,3,3)
Now PA=5 `rArr (PA)^(2)=25`
`rArr (3r-2-1)^(2)+(2r-1-3)^(2)+(2r+2-3)^(2) =25`
`rArr (3r -3)^(2) +(2r -4)^(2) +(2r)^(2) =25`
`rArr 17r^(2) -34r =0 rArr 17r(r-2) =0`
`rArr r-0 " or " r=2`
r=0 `rArr ` the requried point is P(-2 ,-1,3)
r=2`rArr ` the required point is P(4,3,7)
Hence the required point are (-2,-1,3) and (4,3,7)
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