In this exercise you are to find the area of a triangle in R³ in 4 ways, given the points A, B, and C. Plot the points A= (0,2,6), B= (8,2,2), and C= (5,6,4) in Geogebra and 1) Use the polygon command: Polygon(A,B,C) --this will give the lengths of the 3 segments of the triangle and then give the area of this triangle 2) Using Heron's Formula: A = √s (s — a) (s –— b) (s · - c) where s = of the triangle are a, b, c (these are given in the Polygon command in step 1) and the sides a+b+c 2 3) Find the vector from point to A to B and the vector from A to C, i.e. find AB compute the value A = |AB ® AC| and AC and AC
In this exercise you are to find the area of a triangle in R³ in 4 ways, given the points A, B, and C. Plot the points A= (0,2,6), B= (8,2,2), and C= (5,6,4) in Geogebra and 1) Use the polygon command: Polygon(A,B,C) --this will give the lengths of the 3 segments of the triangle and then give the area of this triangle 2) Using Heron's Formula: A = √s (s — a) (s –— b) (s · - c) where s = of the triangle are a, b, c (these are given in the Polygon command in step 1) and the sides a+b+c 2 3) Find the vector from point to A to B and the vector from A to C, i.e. find AB compute the value A = |AB ® AC| and AC and AC
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:In this exercise you are to find the area of a triangle in R³ in 4 ways, given the points A, B, and C.
Plot the points A= (0,2,6), B= (8,2,2), and C= (5,6,4) in Geogebra and
1) Use the polygon command: Polygon(A,B,C)
--this will give the lengths of the 3 segments of the triangle and then give the area of this triangle
2) Using Heron's Formula: A = √s (s − a) (s — b) (sc) where s =
—
a+b+c
2
and the sides
of the triangle are a, b, c (these are given in the Polygon command in step 1)
→
→
3) Find the vector from point to A to B and the vector from A to C, i.e. find AB and AC and
compute the value A =
|AB & AC|
4) Find point D where D is a point on AB where AD 1 CD. Then compute A
=
|AB||CD|
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