Cathy Fulkerson Ajamie

I live in St. Johnsbury, VT, located in the Northeast Kingdom, aka the NEK. My first love was biology. When I was a little girl I roamed the woods around my house during all seasons, went fishing and hunting with my dad and camped a lot. I became interested in teaching after I had children.

I am a middle school math and science teacher working on a M.Ed. Math Grades 7-12 at PSU. I'm also taking Calculus III at Lyndon State College, which is located in the NEK. I just finished my student teaching practicum during the Fall semester 2009 at St. Johnsbury Academy - an awesome private high school located in the NEK. Check it out here http://www.stjacademy.org/

For a long time I wanted to be a science teacher. The Vermont middle school teaching license requires candidates to be certified in two content areas and I chose math as my second area. I discovered that I love learning math. In fact, I have enjoyed it so much, I decided to teach math instead of science.

When I'm not teaching or taking classes, I love to hike, camp, run, cross-country ski, canoe and hang out with my friends. I hurt my knee about two years ago when I flipped over my bike and I recently re-injured my knee doing the limbo. I'm beginning to run again, finally. My profile pic is from Webster Cliffs in Crawford Notch. My daughter and I were attacked by a Canada Jay… we drew in the monster using the app Doodle Buddies, on our Touch iPods.

Oh, I have three kids - they are 26, 24 and 17. So, don't try to pull anything with me - I've seen it all:)

Last night I emailed my calc prof using $\LaTeX$. I'm glad to help anyone with $\LaTeX$.

page 674, # 33
Find the equation of the plane. $x$-intercept is $a$, $y$-intercept is $b$ and $z$-intercept is $c$.

The 3 intercepts are 3 points:

$a(a,0,0), b(0,b,0), c(0,0,c)$

$\overrightarrow{v} = <-a,b,0>$
$\overrightarrow{w} = <-a,0.c>$

$\overrightarrow{v} \times \overrightarrow{w} = <bc, ca, ab>$

Arbritrary vector is $<x-a, y-0, z-0> = <x+a, y, z, >$.

$<bc, ca, ab> \cdot <x-a, y, z, >$ = $<xbc - abc + cay + abz>$ = $0$

It now appears that to factor out the $-abc$, we multiply through by $1 \over abc$ and add $1$ to both sides of the equation.

So, the equation of the plane is;

$x \over a$ + $y \over b$ + $z \over c$ = $1$.

Just want to make sure I'm arriving at the answer correctly. It definitely looks correct to me.

Please note that I didn't use the correct symbol for the vectors… I was just being lazy. It happens.

page revision: 16, last edited: 11 Feb 2010 22:32