The distance between the plane →r.(^i+5^j+^k)=5 and the line →r=2^i−2^j+3^k+λ(^i−^j+4^k) is
A
10√3
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B
102√3
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C
103√3
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D
103
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Solution
The correct option is C103√3
Observe that (i+5j+k).(i−j+4k)=0 ⇒ Line is ∥ to the plane ∴ required distance = distance from (2,−2,3) to the plane x+5y+z=5 is =|2−10+3−5|√1+25+1=103√3