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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)
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
stude
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 +
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 student
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 pro
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 student
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
studen
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
studen
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
stude
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
studen
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
stude
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
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 readi
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 ot
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: Plu
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 o
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 mas
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
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
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
studen
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 d
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
a
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
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
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
stude