(a) Find: (i) The coordinates of N and M (ii) The magnitude of NM, (b) Express vector NM in term OB. Point M is the midpoint of AB and N is the midpoint of OA.

The position vectors A and B with respect to the origin O,(-8,5) are (12,-5)and respectively. Rotate the system counterclockwise about the origin by 20 Vector B = (12m)i + (8m)j on that same coord system. Vector A has a magnitude 12m and is angled at 60 degrees counterclockwise from the positive direction of the x axis of an xy coord. Find the coordinates (x, y, z) of Osaka,Īn xyz-coordinate system is placed with its origin at the center of the earth, so that the equator is in the xy-plane, the North Pole has coordinates (0, 0, 3960), and the xz-plane contains the prime meridian, which is the great semicircle that runsĪn xyz-coordinate system is placed with its origin at the center of the earth, so that the equator (consisting of points with 0-degree latitude) is in the xy-plane, the North Pole (the only point with 90-degree latitude) has coordinates (0, 0, 3960), and The point A(-8,-2) is dilated about the origin by a scale factor of k=1/2 find the coordinates of A after the dilationĪn xyz-coordinate system is placed with its origin at the center of the earth, so that the equator is in the xy-plane, the North Pole has coordinates (0, 0, 3960), and the xz-plane contains the prime meridian.

270 degrees clockwise