You are here:

Advanced Math/find the area of triangle in linear algebra

Advertisement


Question
I am having difficulty with this problem. Any help would be greatly appreciated.

Consider the triangle A(1, 0, 0), B(0, 2, 0) and C(0, 3, 4).
Find the obtuse angle  of the triangle ABC. Find the area of ABC.

Answer
The line AB = (-1,2,0).
The line AC = (-1,3,4).
It is known that the magnitude of the cross product is the area of the rectangle between them.
The triangle has one half of this area.

The cross product is (2*4 - 0*3, 0*-1 - -1*4, -1*-3 - -1*2).
Since 2*4 = 8 and 0*3 = 0, the x term is 8.
Since 0*-1 = 0 and --1*4 = 4, they y term is 4.
Since -1*-3 = 3 and --1*2 = 2, the z term is 2.

The length of this is sqrt(8+4+2) = sqrt(64+16+4) = sqrt(84).
Since 84 is a little bigger than 81, which is 9, I would guess than answer to be 9.15.

Doing it in Excel gives the true answer as 84^0.5 = 9.16515139 as the area of the parallelogram.
The area of the triangle is 1/2 of this, which is 4.582575695.
An answer of 4.58 would probably be good enough.

Advanced Math

All Answers


Answers by Expert:


Ask Experts

Volunteer


Scott A Wilson

Expertise

I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

Experience

Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

Publications
My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Education/Credentials
Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.

©2016 About.com. All rights reserved.