notes / updates
October 3, 2024 | Cross Product with the TI-NSPIRE
tutorial here
September 30, 2024 | Problem 47 in Section 11.3
Hi all, desmos partially agrees with the author's answer to problem 47. The angle itself is the same as the author's (around 40 degrees) but the x-coordinate where this angle occurs is different.
September 27, 2024 | Quiz Notes
Below find some quiz notes. Graded work will be returned in class. If there are mistakes or typos below, feel free to email me.
P1
Let the points be: A(1, 2), B(3,1), and C(8,4). Form three vectors:
\( \vec{AB} = < 2, -1 >, \vec{BC} = < 5, 3 >, \vec{AC} = < 7, 2> \)
Find the three possibilities by adding any vector to the point that wasn't used to form that vector. For example, to the vector \( \vec{OC} \) we add the vector \( \vec{AB} \). The missing points are: (10, 3), (-4, -1), and (6, 5), as shown below:
There were no issues with problem 2, except be sure to use vectors:
If the points of trisection are M and N and the vector connecting the two given points is \( \vec{AB} = < 6, 3 > \), then:
\( \vec{OM} = \vec{OA} + \frac{1}{3}\vec{AB} = <3, 3 > \)
Similarly: \( \vec{ON} = \vec{OA} + \frac{2}{3}\vec{AB} = <5, 4 > \)
Therefore the points are: (3,3) and (5,4).
September 23, 2024 | Quiz Notes
Below find some quiz notes. Graded work will be returned in class. If there are mistakes or typos below, feel free to email me.
P1
Form three vectors using the points: A(4, -2, 7), B(-2,0,3), C(7, -3, 9).
\( \vec{AB} = < -6, 2, -4 >, \vec{AC} = < 3, -1, 2 >, \vec{BC} = < 9, -3, 6 > \)
Note that \( \vec{AB} = -2* \vec{AC} \text{ and } \vec{BC} = (-3/2)* \vec{AB} \)
The three vectors are therefore multiples of each other, so the points are collinear.
Note that the problem asked us to use vectors.
P2
A(2, 9, 1), B(3,11,4), C(0, 10, 12), D(1, 12, 5)
Same idea here, except the four resulting vectors should be two equal pairs:
\( \vec{AB} = < 1, 2, 3 > = \vec{CD} \text{ and } \vec{AC} = < -2, 1, 1 > = \vec{BD} \)
Note that the problem asked us to use vectors.
Here is the SageMath code:
#Problem 2
A=(2,9,1)
B=(3,11,4)
C=(0,10,2)
D=(1,12,5)
#form vectors
AB = vector([B[0]-A[0],B[1]-A[1],B[2]-A[2]])
BC = vector([C[0]-B[0],C[1]-B[1],C[2]-B[2]])
CD = vector([D[0]-C[0],D[1]-C[1],D[2]-C[2]])
AD = vector([D[0]-A[0],D[1]-A[1],D[2]-A[2]])
AC = vector([C[0]-A[0],C[1]-A[1],C[2]-A[2]])
BD = vector([D[0]-B[0],D[1]-B[1],D[2]-B[2]])
print("AB:", AB)
print("BC:", BC)
print("CD:", CD)
print("AD:", AD)
print("AC:", AC)
print("BD:", BD)
plot(AC, start=A) + plot(CD, start=C) + plot(-BD, start=D) + plot(-AB, start=B)
P3 \( t\vec{v} \) consists of all points on the line in the direction of vector \( \vec{v} \), passing through the origin.
\( \vec{u} + t\vec{v} \) describes all points on the lines that passes through the tip of \( \vec{u} \) in the direction of \( \vec{v} \). Here we assume that vector \( \vec{u} \) starts at the origin.
\( s\vec{u} + t\vec{v} \) describes all points on the plane as long as \( \vec{u}, \vec{v} \) are not parallel to each other. If they are parallel, the resulting set is the line passing through the origin in the direction of either vector.
September 22, 2024 | Weekly updates & Current grades
Hi everyone. I write to clarify a couple of things regarding grades and grading.
First, on myCushing under your progress tab you should be able to see your current grade for this course, which is a weighted average of the assessments we have written so far. While individual quiz scores will not be published on myCushing, the current grade will be updated approximately once week.
Second, when you read your weekly update, be sure to check the comments as well as the grade. Sometimes I add individual feedback based on recent performances or in-class observations.
As always, let me know if you have any questions.
September 10, 2024
If you haven't yet, be sure to install a recent version of Geogebra: https://www.geogebra.org/download
September 1, 2024
Hi everyone. In this area of the course page we will post notes, solutions, reminders, and links to other resources throughout the year. Entries will be dated with the most recent posted at the top of the page.