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Find the coordinates of a point on th...

Find the coordinates of a point on the `(x-1)/2=(y+1)/(-3)=z` atg a distance `4sqrt(14)` from the point `(1,-1,0)dot`

A

(9,-13,4)

B

`(8sqrt14,-12,-1)`

C

`(-8sqrt14,12,1)`

D

`(-7,11,-4)`

Text Solution

Verified by Experts

The correct Answer is:
D
Given equation of line in `(x-1)/(2) = (y +1)/(-3) = z = r`
Any point on given lines is `p(2r + 1, -- 3r - 1,r)`, its distance form `(1,-1,0)`
`rArr " "(2r)^(2) + (-3r)^(2) + r^(2) = (4 sqrt(14))^(2)`
`rArr" "r = pm 4` ,
`rArr` Coordinates are `R(9,-14,4) and S(-7,11,-4)` and nearer to the origin is `(-7,11,-4)`
`[{:(,OR = sqrt((9)^(2) +(-13)^(2) +(4))= sqrt(266)),(,and OS = sqrt((-7)^(2) +11^(2) +(-4)^(2))= sqrt(186)):}]`
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