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Find the perpendicular distance of the p...

Find the perpendicular distance of the point (3, -1, 11) from the line `x/y=(y-2)/(-3)=(z-3)/4` .

A

`sqrt(33)`

B

`sqrt(53)`

C

`sqrt(66)`

D

`sqrt(29)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given line passes through the point `A(0,2,3)` and has direction ratios proportional to 2,3,4.
`AM=` Projection of `vec(AP)` on the line
`impliesAM=vec(AP)((2hati+3hatj+4hatk))/29`

`impliesAM=(3hati-3hatj+8hatk).((2hati+3hatj+4hatk))/(sqrt(29))=(6-9+32)/(sqrt(29))=sqrt(29)`
`AP-|vec(AP)|=sqrt(9+9+64)=sqrt(82)`
`:.PM=sqrt(AP^(2)-AM^(2))=sqrt(82-29)=sqrt(53)`
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