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Identify the choice that best completes the statement or answers the question. 1. A line has slope 5 and x-intercept -2. Find a vector equation of the line. a. [x, )] = [3, 2] + #[-2, 0] c. [x, )] = [-2, 0] + 1[2, 3] b. [x, x] - [-2, 0] + 1,1 d. [x, )] = [-2, 0] + 1[3, 2] 2. Write the scalar equation of the plane with normal vector , = [0, -1, 3] and passing through the point (5, -2, 3). a. y - 3z + 11 = 0 c. -Y+ 3z+ 11 = 0 b. y - 3z - 11 = 0 d. -y+ 32 + 16 - 0 3. In three-space, find the intersection point of the two lines: [x, y, =] = [-1, 2, 0] + /[3, -1, 4] and [x, y, =] = [-6, 8, -11 + 1[2, -5, -3]. a. (-1, 2, 0) C. ( 4, 3, -4) b. (-6, 8, -1) d. (3, 2, 1 ) 4. Determine the distance between the point (1, 0, 1) and the plane [x, y, =] = [1, 2, 3] + s[2, 1, 3] + {[4, 2, 0]. a. 1.79 units c. 2.67 units b. 3.14 units d. 1.03 units x = 1+ 5. Determine the distance between the point (4, 3, 2) and the plane {y = 2 + 5 |2 = 3+5+1 a. 3.69 units 2.01 units b. 1.45 units d. 2.89 units x = 2+t x = 3+5+t 6. Determine the distance between the line () = 5- and the plane ( y = 2-s - Z = -4 2 =1+5-t a. 2.33 units C. 1.41 units b. 5.12 units d. 0.34 units 7. Determine the distance between the line [x, y, =] = [4, 5, -2] + /[1, 1, -1] and the plane [x, y, =] = [2, 4, 3] + $[3, 2, 0] + r[1, 0, 2]. a. 3.48 units . 7.22 units b. 9.11 units d. 1.60 units8. Determine the point of intersection of the three planes 1:X+3y-z+9=0 T X- y+z - 11 =0 13: [x, y, =] = [1, 0, 1] + s[2, 1, -1] + /[4, 0, -1]. a. (1, -4, 3) C. (5, -4, 2) b. (5, 0, -5) d. (5, 11, -12) Communication [13 marks] True/False Indicate whether the statement is true or false. 9. A normal vector to a line is parallel to that line. 10. There is no symmetric form for the equation of a plane. 1 1. A plane written in scalar form can be written in vector form. 12. In three-space there are two possibilities for the intersection of two lines. 13. A line will never intersect with a plane. Matching Match the equation of each plane to its scalar form. A X-y- 2z+4 = 0 D 13x - 7y+ 2z + 16 = 0 B Y - 2 E 2x - y- 2z - 6 -0 Y-2-6-0 20. [x, y. =] = [3, 2, 1] + s[2, 0, 3] + ([3, 0, 2] 21. [x, y. =] = [5, -2, 3] + s[3, -2, 4] + 1[5, -2, 6] x = 3 +5 22. y - 2-1-5s z = 1+ 2/ + 35 23. [x, y. =] = [5, 4, -2] + $[2, -1, -1] + z[1, 3, 3] x = -1+ 25 24. y - 2-1+45 2=-1+3/+5