Question 8 (Mandatory) (1 point) The parametric equations of a plane are x=l+23+t J'= 3'3"" 33. Find a normal vector to the z=4+s+3 plane. O a) [1, 3, 2] O b) [1, 3,4] O C) {5, -3, 7] Q d) [2, 1, 1] Question 7 (Mandatory) (1 point) The equation of a plane is x+ 25V+ 32' 5 = '3. Find the y-intercept of the plane. Question 5 (Mandatory) (1 point) A plane passes through the origin and has the direction vectors [1, 2, 3] and [-1, 3, - 2]. Find a scalar equation of the plane. a) 13x+ y- 5z = 0 (b) x+ 2y + 32 = 0 Oc 13x + y- 5z = 9 Od) -x+ 3y-2z =0Question 2 (Mandatory) (1 point) Write the scalar equation of the plane with normal vector # = [5, -1, -2] and passing through the point (5, -1, -2). ( a) 5x - y- 2z = 0 ( b) 5x- y- 2z - 30 = 0 O c) 5x - y- 2z - 25 = 0 O d) 5x- y- 2z + 30 = 0Question 3 (Mandatory) (1 point) A plane passes through the three points A(1, 1, 1), B(2, 3, 4), and C(1,0,1). Find a vector equation of the plane. 0 3) ix. y, 2]= [1,1,1]+ s[1, 2, 3] + [[0, 1,0] 0 b) [x,y,z] = [1, 1, 1] +s[l, u, 1] +1[1, 2, 3] O c) [x,y,z] = [1, 1, 1] +s[2, 3, 4] +1[1, u, 1] Q d) [x,y,z] = [1, 2, 3] +s[2, 3, 4] +1[1, u, 1] Question 6 (Mandatory) (1 point) The vector equation of a plane is [x, y, z] = [1, 1, 1] + s[2, 1, 3] + #[-3, 2, 4]. Find a scalar equation of the plane. a) 2x + 17y - 72 = 0 ( b) 2x + 17y - 7z + 12 = 0 O c) 2x + y+ 32 + 3 =0 O d) x+ y+2+10 = 0A plane passes through the three points A(1, 1, 1), B(2, 3, 4), and C(1, 0, 1). Find a parametric equation of the plane. O a ) x = 1 + 25 y = 1+ 35 -t z = 1+45 O b) x = 1+5 y = 1 + 25 - t z = 1+35 O c) x = 1 + 2s +t y = 1+ 35 Z = 1+4s+t O d) x = 1+5+ 1 = 2+ 2s + 2t Z = 3+ 35 + 35