8. Determine the point of intersection of the three planes ₂x+3y-z+9-0 ₂X-y+2-11-0 : [x, y, z] = [1, 0, 1] + s[2, 1, −1] + [4, 0, -1]. a. (1,-4,3) b. (5,0,-5) 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. 11. A plane written in scalar form can be written in vector form. 20. 12. In three-space there are two possibilities for the intersection of two lines. 13. A line will never intersect with a plane. 21. Matching Match the equation of each plane to its scalar form. x-y-2z+4-0 A D B 2x-y-22-6-0 y-2 E y-2-6-0 C 22. c. 23. d. 24. (5,-4, 2) (5, 11,-12) x=3t+s y-2-1-58 2=1+2+35 13x-7y+22+16-0 [x, y, z] = [3, 2, 1] + s[2, 0, 3] + t[3, 0, 2] [x, y, z] = [5, -2, 3] + s[3, −2, 4] + t[5, -2, 6] [x, y, z]= [5, 4, -2] + s[2, −1, −1] + t[1, 3, 3] [x = -t+25 y-2-1+45 z=-1+3t+s

Fig: 1