App Knowledge/Understanding (8 marks) Identify the choice that best completes the stateme Multiple Choice: 1. A line passes through the points M(0, 1, 4) and N(1, 4, 5). Find a vector equation of the line a. [x, y. z] - [0. 1, 4] + 11. 4. 5]. TER [zy.z] - [1. 3, 1] +41. 4. 5].CER b [x x.z] - [1. 3. 1] + 10. 1, 4]. TER [x y.=] - [0. 1. 4] +41, 1, 1].CER 2. A line has x-intercept 7 and 2-intercept 5. Find a vector equation of the line. a [x. y. =] - [0, 0, 5] + 1-7. 0, 0]. TER c. [x x. z] - [-7.0, 5] + 10, 4 5).tER b. [x, ). z] - [0, 0, 5] + 4-7. 0, 5],TER [x y.=] - [-7. 0, 5] +47. Q, 0).tER 3. Write the scalar equation of the plane with normal vector # - [0, -1, 0] and having a j-intercept 3. a 7+3-0 x+2+3-0 y-3-0 3y- 3-0 4. The vector equation of a plane is [x, y. z] - [1, 1. 1] + s[2 1. 3] + /{-3, 2, 4], s. te R. Find a scalar equation of the plane. a. 2x + y+12+3-0 2x + 17y-72 -12 = 0 2x + 17y - 72 + 12 =0 xty+z+10 =0 5. A 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. x - 1+ 2 x - 1+25 +1 y = 1+ 35-1 S,tER C. ) = 1+ 35 STER z = 1+45 z = 1+45+1 x - 1+s b. y = 1+25-1 STER d. y = 2+ 25+ 21 SitER z = 1+35 z= 3+35+35 6. Find the intersection point of the two lines: [x, y] = [1, 2] + (2, -1] and [x, y] = [0, 3] + s[3, -2]. S,tER. a. [3, 1] [1, 2] h [0, 3] d. [1, 3] x = 3-1 7. In three-space, find the intersection point of the two lines: [x, ), =] = [-2, 3, -3] + s[1, -1, 2], s e R and y = -5+21, tER. z - 7-21 a. (0, 1, 1) C. (-1, 2, -2) b. (-2, 3, -3) d. (3, -5. 7) (5, -1, -2). 8. Write the scalar equation of the plane with normal vector # = [5, -1, -2] and passing through the point a. 5x- y- 22=0 C. 5x- y-2z +30= 0 b. 5x- y-2z-30 = 0 d. 5x-y-22-25=0