1. Find an equation for the plane that contains the line at) : (2 + 3t, 1 + 6t,1 t) and is perpendicular to th plane x + 33; z : 63. 2. Find the distance from the point (2, 4, 7) to the plane 532 + 33; + 22 = 12. 3. Determine whether the following lines intersect the plane 5:}: 4y z = 4, if so describe the intersection. . t) : {1 + 2t,4t, 7 10:) . {t)={1t,3,25t) . {t)={1t,,25t) 4. Consider A - (9 1 6 ) . 8- (3 53 20.0- 00 - Which of all possible products of the above matrices are defined? Compute two of those products. 5. Cosider the f(x, y) = 2x +y+1, (a) Draw (or explain why you cannot draw) the level curves for c = -1, 0, 2, 4. (Annotate the axis, label each level curve and label at least one point on each level curve.) (b) Is the graph of f in R2 or R3? What kind of shape is the graph of f?2 5. Consider 9(13, 3;) = $3 +2312 l. (a) Draw (or explain why you cannot draw) the level curves for c = 2, 1, 1, 7. (Annotate the axis, label each level curve and label at least one point on each level curve.) Hint: it may help to rst sketch g + r: = 1. '|"""|' ll 1rII 1-"|| (b) Is the graph of g in R2 or R3? Sketch the graph of g{;r, y). 7. Consider h(;r,y, z) 2 $2 + y2 + 22. Do the level sets of h live in R2 or R3? Does the graph of h live in R2, R3, R4, or R5? Draw (or explain why you cannot draw) the level curves for c : 2, 0, 4, 9