MATH 2163 Quiz: MATH 2163 OK State Quiz8
Quiz # 1– Math 2163, Calculus III – Aug 31, 2007
Show all your work neatly and concisely, and indicate your final answer clearly.
1. (3pts) Find symmetric equations of the line through the origin and parallel to the line
x= 2t,y= 1 −t,z= 4 + 3t.
Solution: The line should pass through the origin (0,0,0) and has the direction
<2,−1,3>. So its symmetric equation can be written as
x−0
2=y−0
−1=z−0
3.
(You can find the formula of symmetric equation in page 859 of the textbook.)
2. (2pts) Find the linear equation of the plane through the point (−2,8,10) and parallel
to the plane x+y+z= 2.
Solution: The plane should pass through point (−2,8,10) and has a normal vector
<1,1,1>. So its scaler equation should be
1(x−(−2)) + 1(y−8) + 1(z−10) = 0.
(See the formula on page 862 of the textbook.) Simplify the above equation and get
x+y+z−16 = 0.
