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Math 253 Midterm Exam
1. (a) Consider the line with parametric equations: x = 2 + 2t, y = 1 + 5t,
Find the point in which this line meets the plane: x y + z = 3.
z = 4t.
[6]
(b) Find the equation of the line perpendicular to the abov
Assignment #8 MATH253-104
This assignment is due Friday, November 19th in class. No late assignments will be
accepted. Show all work and reasoning in completing the questions. Working with other
students is encouraged, but copying answers will not be tole
Assignment 1 - Due Sep 24th
1. Given two vectors a and b illustrate geometrically (draw)
c = 4a + 3(b a).
2. If a and b are two nonzero vectors which do not have the same direction, prove that
c = a + b is a vector in the same plane determined by a and b.
Assignment #3 MATH253-104
This assignment is due Friday, October 8th in class. No late assignments will be accepted.
Show all work and reasoning in completing the questions. Working with other students is
encouraged, but copying answers will not be tolera
Assignment #1 MATH253-104 Solution
1)
2) Need to show
Now since ,
So
are orthogonal to
.
, we know
3) For the two vectors to be perpendicular, we need their dot product to be zero.
4)
, and so the projection is
5)
,
, and so
=
Therefore
6) No it doesnt. F
Assignment #2 MATH253-104
This assignment is due Friday, October 1st in class. No late assignments will be accepted.
Show all work and reasoning in completing the questions. Working with other students is
encouraged, but copying answers will not be tolera
Assignment #4 MATH253-104
This assignment is due Friday, October 15th in class. No late assignments will be
accepted. Show all work and reasoning in completing the questions. Working with other
students is encouraged, but copying answers will not be toler
Assignment #5 MATH253-104
This assignment is due Friday, October 29th in class. No late assignments will be
accepted. Show all work and reasoning in completing the questions. Working with other
students is encouraged, but copying answers will not be toler
Assignment #7 MATH253-104
This assignment is due Friday, November 12th in class. No late assignments will be
accepted. Show all work and reasoning in completing the questions. Working with other
students is encouraged, but copying answers will not be tole
Assignment #6 MATH253-104
This assignment is due Friday, November 5th in class. No late assignments will be
accepted. Show all work and reasoning in completing the questions. Working with other
students is encouraged, but copying answers will not be toler
Assignment #8 MATH253-104
This assignment is due Friday, November 19th in class. No late assignments will be
accepted. Show all work and reasoning in completing the questions. Working with other
students is encouraged, but copying answers will not be tole
Assignment #7 MATH253-104 - Solutions
This assignment is due Friday, November 12th in class. No late assignments will be
accepted. Show all work and reasoning in completing the questions. Working with other
students is encouraged, but copying answers will
MATH 253 Section 104 Winter 2010 Midterm Solutions
You have 50 min to solve 4 problems. Please note
Write your name/student id clearly
Illegible work will have marks removed. If I have trouble reading your work,
I wont mark it.
Write only on one side o
Assignment #6 MATH253-104 Solutions
This assignment is due Friday, November 5th in class. No late assignments will be
accepted. Show all work and reasoning in completing the questions. Working with other
students is encouraged, but copying answers will no
Solutions to Math 253 Midterm Exam
1. (a) Consider the line with parametric equations: x = 2 + 2t, y = 1 + 5t, z = 4t.
Find the point in which this line meets the plane: x y + z = 3.
[6]
Solution: Plug the parametric equations into the equation of the pla
SOLUTIONS TO QUIZ #4, Math 253
1. Determine the volume of the solid that lies above the rectangle 0 x 1, 0 y 2
in the x, y plane and below the surface z = 5 x2 y 2 .
Solution: Notice that 5 x2 y 2 0 on the rectangle 0 x 1, 0 y 2. The
volume is
x=1
y =2
x=
SOLUTIONS TO QUIZ #5, Math 253
1. Find the mass and center of mass of the lamina that occupies the region bounded by
the lines y = x, y = x, x = 1 if the density is (x, y) = x.
Solution: The total mass is
(x, y)dA (where D is given by 0 x 1, x y x)
m =
D
Assignment #10 MATH253-104
This is what the assignments for the remaining sections would be if I had time to give
them. They cover the material from Sections 16.6-16.9. It is not to be handed in, but I
recommend trying them as if it was an actual assignme
Assignment #10 MATH253-104 - Solutions
1) Find the mass of the crust of the earth if the crust has density function which is
the reciprocal of the cube of the distance to the center of the Earth. The earth crust
is 40km thick and the radius of the earth (
Assignment #4 MATH253-104
This assignment is due Friday, October 15th in class. No late assignments will be
accepted. Show all work and reasoning in completing the questions. Working with other
students is encouraged, but copying answers will not be toler
Assignment #3 MATH253-104 - Solutions
1) Find and sketch the domain of the function
Write the domain in set notation.
.
We need
and
. The latter equation gives
and the first gives
. Hence we get the domain
. As for the sketch, its the part of the x-y plan
Assignment #2 MATH253-104 - Solutions
1) Find parametric and symmetric equation for the line:
a) Passing through points
and
The vector parallel to the line is
vector equation is
equations
and so the
and so we get the parametric
where
Solving for in each o
Assignment #9 MATH253-104 - Solutions
This assignment is due Friday, November 26th in class. No late assignments will be
accepted. Show all work and reasoning in completing the questions. Working with other
students is encouraged, but copying answers will
Assignment #5 MATH253-104 - Solutions
This assignment is due Friday, October 29th in class. No late assignments will be
accepted. Show all work and reasoning in completing the questions. Working with other
students is encouraged, but copying answers will
Assignment #9 MATH253-104
This assignment is due Friday, November 26th in class. No late assignments will be
accepted. Show all work and reasoning in completing the questions. Working with other
students is encouraged, but copying answers will not be tole