Question 1: this is from my 'Vector Equation of a Line' lesson. I have attached the answers as well.

A line has the equation 3? = is: + 9. a} Give a direction vector for a line that is parallel to this line. h] Give a direction vector for a line that is perpendicular to this line. c] Give the coordinates of a point on the given line. d} In both vector and parametric form, give the equations of the line parallel to the given line and passing through AWE). e} In both vector and parametric form, give the equations of the line perpendicular to the given line and passing through 3 [2,1). 4. State where possible vector, parametric, and symmetric equations for each of the following lines. a) The line passing through the point P(-1,2,1) with direction vector (3, -2,1) b) The line passing through the point B(-2,3,0) and parallel to the line passing through the points M(-2, -2,1) and N(-2,4,7). c) The line passing through the point Q(1,2,4) and parallel to the z-axis.1. a. m (6, -5) b. n = (5, 6) C. (0, 9) d. = (7,9) + 1(6, -5), ER; 7 + 6, y = 9 - 5t, teR e. = (-2, 1) + 1(5, 6), tER; X 3-2 + 5ty = 1 + 6,/ERb. 7 = (-1, 1, 0) + #(0, 1, 1), tER; x = -1, y = 1 +t, z = t, teR; y - 1 _ 1 c. F = (-2, 3, 0) + +(0, 1, 1), tER; x = -2, y = 3 + t, z = t, tER; y - 3 _2 x 1 i,x = -2 d. 7 = (-1, 0, 0) + f(0, 1, 0), tER; x = -1, y = t, z = 0, tER; Since two of the coordinates in the direction vector are zero, there is no symmetric equation for this line. e. r = 1(-4, 3, 0), tER; x = -4t, y = 31, z = 0, fER; X = 2:2 =0