Find the distance of the point `(1, 2-1)` from the plane `x -2y + 4z - 10 = 0`.

Explanation

The distance of the point `(x_(1), y_(1), z_(1))` from the plane ` ax + by + cz + d = 0` is given by
` |(ax_(1) + by_(1) + cz_+(1) + d)/(sqrt(a^(2) + b^(2) + c^(2)))|`
Here, ` (x_(1) , y_(1) , z_(1)) = (1, 2, -1) and a= 1, b = - 2, c = 4, d = - 10 .`
` :. ` The required distance = `|(1 xx1 + 2 xx (-2) + 4 (-1) - 10)/(sqrt(1^(2) + (-2)^(2) + 4^(2)))|`
` = |(1 - 4 - 3 - 10)/sqrt(1 + 4 + 16)|`
` = |(-17)/21|`
` = 17/sqrt21 ` units.