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

Answer 1

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