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Find the Length of the Perpendicular from Origin to the Plane - Mathematics

Sum

 Find the length of the perpendicular from origin to the plane `vecr. (3i - 4j-12hatk)+39 = 0`

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Solution

`vecr. (3i - 4j-12hatk)+39 = 0`
`3x - 4y - 12z + 39 = 0`

Perpendicular length from origin to plane
=` |(39)/ (sqrt(3^2 + 4^2+ 12^2))|`

=`| (39)/(sqrt(9+16+144))|`

= `|39/sqrt(169)|`

`= |3|`
`= 3  unit`

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