The distance of the line `vec r=2 hat i-2 hat j+3 hat k+ lambda( hat i- hat j+4 hat k)` from the plane `x+5y+z=5` is ?

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Q 1317323280.     The distance of the line `vec r=2 hat i-2 hat j+3 hat k+ lambda( hat i- hat j+4 hat k)` from the plane `x+5y+z=5` is ?
A

`frac{3}{10}`

B

`frac{10}{9}`

C

`frac{10}{3}`

D

`frac{10}{3 sqrt 3}`

HINT

A point on the given line `vec r=(2hat i-2 hat j+3 hat k)+lambda(hat i-hat j+4hat k)` is `A(2,-2,3)`

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

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