MODEGEO Problem Set no.1 1. Given the line . a. b. c. d. e. f. = (1, 3) + [ (3, 4) ], do the following: Find a unit direction vector of . Find a normal vector of . Find a point on other than (1, 3). Determine whether the point (2, 4) lies on . What is the slope of ? Find a cartesian equation for . 2x 3y = 6, do the following: 2. Given the line a. b. c. d. Find a direction vector of . Find a normal vector of . Write the equation of in point-direction form. . Find an equation of a line (in point-direction form) which passes through the origin and is parallel to line . 3. Given the points P = (1, 1) and Q = (8, 7) on a line , do the following: a. Find the midpoint of PQ . b. Find an equation of . Write the answer in point-direction form. 7 24 , and w = 25 25 4. Given that v = 24 7 , , 25 25 a. Show that { v, w } is an orthonormal pair. b. If X = (2, 1), find scalars c and d such that X = cv + dw