Project b = (1,0,0) onto the lines through a₁ and a2 in Problem 5 and also onto = a3 (2,1,2). Add up the three projections P₁ + P₂ + P3.

Find k so that the line through (4,1) and (k,2) is a. parallel to 2x+3y=6, b. perpendicular to 5x2y=1. c. d.

Use slopes to show that the square with vertices at (2,5), (4,5), (4,1), and (2,1) has diagonals that are perpendicular.

Three of the four vertices of a parallelogram are 0,-2, 6,8, and 10,1. Find the possibilities for the coordinates of the remaining vertex.