Find a unit vector perpendicular to the plane ABC where A,B,C are point (1,1,2),(2,3,5) and (1,5,5).

Find a unit vector perpendicular to the plane ABC where A,B,C are the points (3,-1,2)(1,-1,-3)(4,-3,1) respectively.

Find the area of the triangle with vertices A(1,1,2),B(2,3,5) and C(1,5,5).

Find the equation of the plane passing through (1,1,-1),(2,3,5) and (-1,4,-5).

Show that the line through the points (1,-1,2), (3,4,-2) is perpendicular to the line through the points (0,3,2) and (3,5,6).

Find the unit vector in the direction of vector vecP Q , where P and Q are the points (1,2,3) and (4,5,6) respectively.

Consider three points on space (2,1,0),(3,-2,-2) and (3,1,7) Find the Cartesian equation of the plane passing through the above points. find a unit vector perpendicular to the plane and also find the perpendicular distance of the plane from the origin..

Find the distance between the points (2,3,5) and (4,3,1) .

Find the unit vector in the direction of oversetrarr(PQ) , where P and Q are the points (1,2,3) and (4,5,6) respectively.

Find the Cartesian equation of the plane passing through the point A(2,5,-3) , B(-2,-3,5) and C(5,3,-3).

Find the vector and cartesian equations of the plane which passes through the point (5,2,-4) and perpendicular to the line with direction ratios 2,3,-1