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

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

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.

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 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 distance between the points P(-2,4,1) .and Q(1,2,-5) .

Find the distance between the points P(1,-3,4) and Q(-4,1,2) .

If A and B are 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 centroid of the triangle ABC is at the point (1,2,3) . If the coordinates of A and B are (3,-5,7) and (-1,7,-6) respectively. Find the coordinates of the point C.

Find the locus of the set of points P such that the distance from A(2,3,4) is equal to twice the distance from B(-2,1,2) .

Find the vector joining the points P(2,3,0) and Q(-1,-2,-4) . directed from P to Q .