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 point P such that its distances from the points A(3,4,-5) and B(-2,1,4) are equal

Find the locus of a point P such that 3bar(PA^2)=2bar(PB^2) where A(1,1,4) & B (2,1,3)

Find the cosine of the angle between the lines BA and BC where A, B, C are the points (1, 2, 3), (2, 5, -1) and (-1, 1, 2) respectively.

P is a point on bar(AB) such that bar(AP)=3bar(PB) . If the coordinates of A and B be (3, -4) and (-5, 2) respectively, find P.

P is a point on the line - segment overline(AB) such that overline(AP)=overline(3PB) , if the coordinates of A and B are (3,-4) and (-5,2) respectively , find the coordinates of P.

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.

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.

A point P(x ,y ,z) is such that 3P A=2P B , where Aa n dB are the point (1,3,4)a n d(1,-2,-1), irrespectivley. Find the equation to the locus of the point P and verify that the locus is a sphere.

Find the equation of the plane passing through the point A(1,2,1) and perpendicular to the line joining the points P(1,4,2) and Q (2,3,5) . Also , find the distance of this plane from the line (x+3)/(2)=(y-5)/(-1)=(z-7)/(-1) .

P is a point on the line segment bar(AB) such that AP = PB. If the coordinates of A and B are (3, -4) and (-5, 2) respectively find the coordinates of P.