Find a unit vector perpendicular to the plane determined by the points `(1,-1,2),(2,0,-1) and (0,2,1)dot`

The unit vector perendicular to the plane determined by P (1,-1,2) ,C(3,-1,2) is ________.

Find the equation of the plane passing through the points (2,1,0),(5,0,1) and (4,1,1) .

In each of the following find a unit a vector perpendicular to both vec (a) and vec (b) vec(a) = (2,1,1) and vec(b) = (1,-1,2)

Find the equation of the plane passing through the point(1,2,1) and perpendicular to the line joining the points (2,3,5) and (1,4,2).

Find the equation of the plane passing through the point (1,2,1) and perpendicular to the line joining the points (1,4,2) and (2,3,5). Also find the coordinates of the foot of the perpendicular and the perpendicular distance of the point (4,0,3) from the above found plane.

Find the equation of the plane which passes through the points (1,2,3),(2,3,1) and (3,1,2)

Find the equation of the plane which passes through the points (1,2,3) ,(2,3,1) and (3,1,2).

Find the distance between the point (1+sqrt2,1-sqrt2) and (0,0)

Find the equation of the plane passing through the points (2,1,0),(5,0,1) and (4,1,1) If P is the point (2,1,6) then find point Q such that PQ is perpendicular to the above plane and the mid point of PQ lies on it.

By vector method find the area of the triangle whose vertices are (1,1,1) ,(2,0,1) and (3,-2,0)