MATH 20550: Calculus III
Practice Exam 1
Multiple Choice Problems
1. Find an equation for the line through the point (3,โ1,2) and perpendic-
ular to the plane 2xโy+z+ 10 = 0.
(a) xโ3
2=y+1
โ1=zโ2 (b) x+3
2=yโ1
โ1=zโ2
(c) xโ2
3=y+1
โ1=zโ2
2(d) 3xโy+ 2z+ 10 = 0
(e) 3xโ2y+z+ 10 = 0
2. Find an equation of the plane that passes through the point (1,2,3) and
parallel to xโy+z= 100.
(a) xโy+zโ2 = 0 (b) xโy+z+2 = 0 (c) x+2y+3z= 100
(d) xโ1 = 2 โy=zโ3 (e) xโ1 = y+1
2=zโ1
3.
3. Find the distance between the point (โ1,โ1,โ1) and the plane x+ 2y+
2zโ1 = 0.
(a) 2 (b) 0 (c) 6 (d) -2 (e) -6
4. Find values of bsuch that the vectors <โ11, b, 2>and < b, b2, b > are
orthogonal
(a) 0, 3, -3 (b) 0, 11, 3 (c) 0, -11, 2
(d) 0, 2, -2 (a) 0, 11, 2
5. Find the area of the triangle with vertices at the points (0,0,0), (1,0,โ1)
and (1,โ1,2).
(a) โ11
2(b) โ11 (c) โ6 (d) โ6
2(e) 1
6. Which vector is always orthogonal to bโprojab.
(a) a(b) b(c) aโb(d) |a|b(e) projba
7. Find the parametric equations of the intersection of the planes xโz= 0
and xโy+ 2z+ 3 = 0.
(a) The line given by x=โt,y= 3 โ3tand z=โt.
(b) The line given by x=โ2โt,y= 1 โ3tand z=โt.
(c) The line given by x= 1 + t,y= 6 โtand z= 1 + 2t.
(d) The plane 3x+ 3yโ3z+ 3 = 0.
(e) The line given by x= 1 + t,y= 6 and z= 1 โt.
8. Find an equation for the normal plane to the vector function
r(t) = hetโ1, t2,cos(1 โt)i
when t= 1.
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