Knowledge I Understanding [8 marks] Identtfv the choice that best completes the statement or answers the question. 2 . A line has slope 3 and x-intercept 2. Find a vector equation of the line. a. [x. r] - [3. 2] + 4-2, 0] c. [L y] - [-2. 01+ t[2. 3] b. d. x, =2,E|+t3,2 [X,y]-[2,U]+1%,1' [y] [ ] [ ] . Write the scalar equation of the plane with normal vector 3? - [0, 1, 3] and passing through the point (5, 2, 3). a. y-33+11-l] c. -y+32+11-l] b, y3z11= d. y+32+16=0 . In three-space, nd the intersection point of the two lines: [x, y, z] = [1, 2, 0] + t[3, 1, 4] and [x, y, z] = [6, 8, 1] + t[2, 5, 3]. a. ('1, 2. 0) Cr- (43 3! 4) b. (6, 8, 1) d. (3. 2. 1) . Determine the distance between the point (1, 0, 1) and the plane [x, y,z] = [1, 2, 3] + s[2, 1, 3] + t[4, 2, 0]. a. 1.79 units c. 2.67 units b. 3.14 units d. 1.03 units x=l+t . Determine the distance between the point (4, 3, 2) and the plane y = 2 + s z=3+s+t a. 3.69 units c. 2.01 units b. 1.45 units d. 2.89 units x=2+t x=3+s+t . Determine the distance between the line y - 5 - t and the plane 3! - 2 - s t . z = 4 z = l + s t a. 2.33 units c. 1.41 units b. 5.12 units d. 0.34 units . Determine the distance between the line [x, y, z] = [4, 5, 2] + t[l, 1, l] and the plane [x, y, z] = [2, 4, 3] +S[3, 2, 0]+t[1, 0, 2]. a. 3.48 units c. 7.22 units b. 9.]1units d. 1.60units 8. Determine the point of intersection of the three planes :1: x+ 3y-z+ 9 = I] 12:xy+zll=0 11:31 [1, y, 2] = [1, 0,1]+ S[2, 1, l] + t[4, 0, l]. a. (1, 4, 3) c" (59 _49 2) b. (5, 0, 5) d. (5, 11,42) Communication [13 marks] TruelFalse Indicate whether the statement is true orfalse. 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. 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-Zz+4=l] D 13x-7y+ 22+16=EI B y=2 E 2x-y22-=0 C yz= 20- [L )6 Z] = [3. 2, 1] + S[2, 0, 3] + t[3, 0, 2] 21. [x, y, z] = [5, 2, 3] + s[3, 2, 4] + t[5, 2, 6] x=3t+s 22. y=2t5s z=l+21+3s 23- [Ll/32]:[5,4,-2]+S[2,-1,-1]+f[1. 3, 3] x--t+25' 24. y=2t+4s z--l+3t+s