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Question
The distance of the plane `vec"r" *(2/7hat"i" + 3/4hat"j" - 6/7hat"k")` = 1 from the origin is ______.
Options
1
7
`1/7`
None of these
Solution
The distance of the plane `vec"r" *(2/7hat"i" + 3/4hat"j" - 6/7hat"k")` = 1 from the origin is 1.
Explanation:
Given that, `vec"r" *(2/7hat"i" + 3/4hat"j" - 6/7hat"k")` = 1
So, the distance of the given plane from the origin is
= `|(-1)/sqrt((2/7)^2 + (3/7)^2 + ((-6)/7)^2)|`
= `|(-1)/sqrt(4/49 + 9/49 + 36/49)|`
= `1/1`
= 1
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