Find the equation of set of points P such that `PA^(2)+PB^(2)=2k^(2)`, where A and B are the points `(3, 4, 5) and (-1,3,-7)`, respectively.

Find the equation of the set of the points P such that its distance from the points A(3, 4, -5) and B(-2, 1, 4) are equal.

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

If A and B be the points (3, 4, 5) and (-1, 3, -7) respectively, find the equation of the set of points P such that PA^(2)+PB^(2)=k^(2) , where k is a constant.

The locus of the moving point P such that 2PA=3PB , where A is (0,0) and B is (4,-3), is

Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, -1).

Find the value of k if the points A(2,3), B(4,k) and C(6,-3) are collinear.

Find the equation of straight line parallel to 2hat(i)-hat(j)+3hat(k) and passing through the point (5, -2, 4) .

Find the equation of the plane passing through the point (-1,2, 1) and perpendicular to the line joining the points (-3, 1, 2) and (2, 3, 4). Find also the perpendicular distance of the origin from this plane.

Find the equation of the plane through the points (2, 1, 0), (3, -2, -2) and (3, 1, 7).