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Question
The perpendicular distance of the plane `bar r. (3 hat i + 4 hat j + 12 hat k) = 78` from the origin is ______.
Options
4
5
6
8
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Solution
The perpendicular distance of the plane `barr. (3hati + 4hatj + 12hatk) = 78` from the origin is 6.
Explanation:
Given plane is `bar r. (3 hat i + 4 hat j + 12 hat k) = 78`
`bar n = 3 hat i + 4 hat j + 12 hat k`
`|bar n| = sqrt((3)^2 + (4)^2 + (12)^2)`
`|bar n| = sqrt(9 + 16 + 144)`
`|bar n| = sqrt 169`
`|bar n| = 13`
∴ `barr.hati = 78/|barn|`
= `78/13`
= 6
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