Please help with this entire document I need help with all the questions s. thw answers are given please help with all the process

MCV4U EQUATIONS OF LINES IN R3 PRACTICE 1) Write a vector equation for a line given each direction vector m and point Po- a) m = [2.-3,5], P.(8,-11.2) b) m = [-3,4.7], P.(7.-1.4) 2) Write the vector equation of the line that passes through each pair of points. a) A(4,-3,1), B(2,-3,7) b) A(5.6, -1), B(0, -3.2) 3)Write the parametric equations for each vector equation. a) [x, y.z] = [0,4,-7] + t[3, -4.1] b) [x, y.z] = [7.5, -4] + +[-2.1,3] 4) Write a vector equation for each line, given the parametric equations. (x = 4+ 3t al tiny = 7- 21 ( x = 4 bley = 5 -9t = =1+: = = -3 5) Write a vector equation and the parametric equations of a line going through the points A(7, 8, -3) and B(-2, 3, 5). 6) Determine the vector equation of a line through Po(-1, -7, 7) and perpendicular to [x, y.z] = [1,-7,3] + t[4, -1.2]. 7) Determine which points are on the line [x, y.z] = [3.1, -4] + +[2.0,5]. a) (-5, 1, -24) b) (19, 1, 37) 8) 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 points (-1,1,0) and B(-1,2,1) c) The line passing through the point Q(1,2,4) and parallel to the z-axis 9) Determine the parametric equations of the line whose direction vector is perpendicular to the direction vectors of the two lines -= 2+10 = #+2 and #-S = >-S = #+ and passes through the point (2, -5,0). Answers 1)a) [x, y, z] = [8, -11, 2] + ([2, -3, 5] b) [x, y, z] = [7, -1, 4] + f[-3, 4, 7] 2)a) [x,y,z]=[4,-3,1]+t[-2,0,6] b) [x,y,z]=[5,6,-1]+t[-5,-9,3] 3) e:(x=3t y=4-4t z=-7+t b) e: (x=7-2t y=5+t z=-4+3t 4)a) [x, y, z] = [4, 7, 1] + ([3, -2, 1] b) [x, y, z] = [0, 5, -3] + t[4, -9, 0] 5) [x, y, z] = [7, 8, -3] + ([-9, -5, 8]; f:(x=7-9t y=8-5t z=-3+8t 6) [x, y. z] = [-1, -7, 7] + t[0, 2, 1] 7)a) Yes b) No 8)a) [x.y.z]=[-1,2,1]+t[3,-2,1]: 6:(x=-1+3t y=2-2t z=1+t; (x+1)/3 = (y-2)/-2 = (2-1)/1 b) [x.y,z]=[-1,1,0]+t[0,1,1]; 6:(x=-1 y=1+t z=t; (y-1)/1 = z/1, x=-1 c) [x,y,z]=[1,2,4]+t[0,0, 1]; e:(x=1 y=2 z=4+t ; no symmetric equation for this line since two of the direction vector coordinates are zero. 9) e: (x=2-34t y=-5+25t z=13t Page 1 of 1