Let P be the point 3 1 2 Suppose that the point P01 2 7 is 1

Let P be the point (-3, 1, -2). Suppose that the point P0(-1, -2, 7) is 1/9 of the way from P to Q. Find the point Q.

P is the point (-3, 1, -2) and P₀ is the point (-1, -2, 7). Then the vector PP₀ is ( 2,-3,9). Therefore, the vector PQ is 9(PP₀) = (18,-27,81). Now, let Q be the point (x,y,z). Then x-(-3)=18 so that x = 15, y-1= - 27 = 1 so that y = -26 and z-(-2) = 81 so that z = 79. Thus the point Q is ( 15,-26,79).