In the following cases, find the distance of each of the given points from the corresponding given plane.

Explanation

We know that the distance of point `P(x_(1),y_(1),z_(1))` to the plane `Ax+By+Cz=D` is
`d = |(Ax_(1)+By_(1)+Cz_(1)-D)/(sqrt(A^(2)+B^(2) +C^(2)))|"………"(i)`
(a) Distance of point `(0,0,0)` from the plane `3x-4y+12z-3=0` is
`d = (|3xx0-4xx0+12xx0-3|)/(sqrt(3^(2)+(-4)^(2)+(12^(2)))) = (|-3|)/(sqrt(9+16+144))`
`= (3)/(sqrt(169)) = 3/13` unit
(b) Distance of point `(3,-2,1)` from the plane `2x-y+2z+3= 0` is
`d=(|2xx3+(-1)xx(-2)+2xx1+3|)/(sqrt(2^(2)+(-1)^(2)+2^(2)))`
`= (|6+2+2+3|)/(sqrt(4+1+4))`
` = (13)/(sqrt(9)) = (13)/(3)` unit
(c) Distance of point `(2,3,-5)` from the plane `x+2y-2z-9=0` is
`d = (|2+2xx3-2xx(-5)-9|)/(sqrt(1^(2)+2^(2)+(-2)^(2))) = (|2+6+10-9|)/(sqrt(1+4+4))`
`= 9/(sqrt(9)) = 9/3 = 3` unit
(d) Distance of point (-6,0,0) from the plane `2x-3y+6z-2=0` is
`d = (|2xx(-6)-3xx0+6xx0-2|)/(sqrt(2^(2)+(-3)^(2)+6^(2))) = (|-14|)/(sqrt(4+9+36))`
`= 14/7 = 2` unit.