SOLUTIONS 1. Put a = P Q = (1, 1, 1), b = R Q = (2, 2, 1). (a) n = a b = (3, 3, 0). Plane 3(x + 3) + 3(y 1) = 0 (b) A = |a b|/2 = 3 2/2 (c) c = T Q = (1, 0, 2), Volume V = (a b) c = 3 2. (a) r (t) = (
MATH 0240 Final Sample Exam 7
Problem 1. Find the minimum distance between the lines
(x, y, z ) = t(1, 1, 1), t R, and (x, y, z ) = (1, 2, 1) + s(1, 0, 1), s R.
Problem 2. Determine all points at whic
MATH 0240 Midterm Examination I Sample 1
This test consists of 11 problems. All work must be shown in order to
get credit. Please write legibly and explain your logic by words whenever
appropriate. If
MATH 0240 Midterm Examination I Sample 2
This test consists of 11 problems. All work must be shown in order to
get credit. Please write legibly and explain your logic by words whenever
appropriate. If
MATH 0240 Midterm Examination I Sample 3
This test consists of 11 problems. All work must be shown in order to
get credit. Please write legibly and explain your logic by words whenever
appropriate. If
MATH 0240 Midterm Examination II Sample 1
This test consists of 8 problems. All work must be shown in order to
get credit. Please write legibly and explain your logic by words whenever
appropriate. If
MATH 0240 Midterm Examination II Sample 2
This test consists of 10 problems, each worth 10 points. All work must
be shown in order to get credit. Please write legibly and explain your logic
by words w
MATH 0240 Midterm Examination II Sample 3
This test consists of 9 problems. All work must be shown in order to
get credit. Please write legibly and explain your logic by words whenever
appropriate. If
Quiz 4
Name
1. Determine the equation of the line having a slope of 3 and passing through the
point (18, 13).
y 13 = 3(x 18)
y = 3x + 67
2. If f (x) = 2x + 1 and g (x) = x2 3x + 5, determine: (simplif
MATH 0240 Final Sample Exam 6
Problem 1. Find the points on the cone z 2 = x2 + y 2 closest to the point
(1, 3, 4).
Problem 2. Express the volume of the tetrahedron with vertices at
points (0, 0, 0),
College Algebra F inal Review
EXAM ONE QUESTIONS
YOU MAY USE
1.
x=-bb2-4ac2a
x+b22=c+b22
Use the square root to solve:
2.
Complete the square to solve:
x2+ 10x+18 =0
3.
Find the imaginary solution:
4
1. Determine whether the following vector elds F have a potential , i.e., whether
F = . Explain your answers.
(a) F = x + 2xy, x2 + 2z, 2x2 + z .
(b) F = 2xy + 2yz, x2 + z 2 + 2xz, 2yz + 2xy
2. Let D
1. (a) Find an equation of the plane determined by the three points P (4, 0, 2),
Q(3, 1, 1) and R(5, 1, 0).
(b) Find the area of the triangle whose vertices are P , Q, R.
(c) Find the volume of the pa
1. Consider the points A(1, 0, 0), B (1, 2, 0), and C (1, 1, 3).
(a) Find (to the nearest degree) the angle ABC .
(b) Find the area of the parallelogram formed by A, B , and C .
(c) Determine whether
Math 240 Final Sample Exam 8
Problem 1. Find parametric equations of the line parallel to the planes
x + y + z = 1 and x y + 2z = 5, and passing through the point (1, 2, 3).
Problem 2. The curve is gi
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