Math 265: Lesson 1 Assignment
1) Let w = 3, w = -1, and w = 1.2. (a) Sketch the vectors w, w, and 2 + w. (b) Find a unit vector in the direction of w.
2) Let P = (2,4), Q = (-1,3), R = (3,8), S = (6,6). Determine if the vectors PQ and RS are parallel.
3) A line in space passes through the points P = (4,0,1) and Q = (-2,3,5). (a) Write down a vector parameterization for the line. (b) Write down parametric equations for the line.
4) Find an equation for the line through the point P = (1,0,-3) and perpendicular to the xy-plane.
5) Determine if the lines r1(t) = (3,0,2+t) and r2(s) = (0,1,-1) + s(4,1,1) intersect, and if they do, find the point of intersection.
6) (Bonus) Suppose a and b are two positive numbers. Find an equation for the line in space passing through a on the x-axis and b on the y-axis.
Each problem is worth 10 points. The bonus is worth up to 5 points.