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

Answer 1

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