Find the value of x such that PQ = QR, where P, Q and R are (6,- 1), (1, 3) and (x, 8) 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.

Find a vector of magnitude 11 in the direction opposite to that of vec(PQ) , where P and Q are the points (1,3,2) and (-1,0,8) 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.

Find a unit vector in the direction of vec(PQ) . where P and Q have coordinates (5, 0, 8) and (3, 3, 2) respectively.

Find the components and magnitude of the vector vec PQ where P and Q are the points (-1,-2,4) and (2,0,-2) respectively.

Find the value of x , if x/3 + 1/6 = x/2 - 1/3

Find the value of r if 5. ^4P_r= 6. "^5P_(r-1) .

A rectangle PQRS has its side PQ parallel to the line y= mx and vertices P,Q, and S on the lines y=a, x=b, and x=-b, respectively. Find the locus of the vertex R.