The distance of the point `(-1,-5,-10)` from the point of intersection of the line `vec r=(2 hat i- hat j+2 hat k)+lambd

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Q 1327023881.     The distance of the point `(-1,-5,-10)` from the point of intersection of the line `vec r=(2 hat i- hat j+2 hat k)+lambda(3hat i+4 hat j+12 hat k)` and the plane `vec r.(hat i-hat j+hat k)=5` is ?
A

`frac{-6}{sqrt 3}`

B

`frac{6}{sqrt 3}`

C

`sqrt {149}`

D

`13`

HINT

Given eqn. of the line is written as `frac{x-2}{3}=frac{y+1}{4}=frac{z-2}{12}=lambda` Any point ` P` on this line can be expressed in terms of `lambda` as `P(3 lambda+2,4 lambda-1,12 lambda+2)`

Solution
(Provided By a Student and Checked/Corrected by EXXAMM.com Team)

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