   Chapter 11.3, Problem 26E

Chapter
Section
Textbook Problem

# Classifying a TriangleIn Exercises 27–30, the vertices of triangle are given. Determine whether the triangle is an acute triangle, an obtuse triangle, or a right triangle. Explain your reasoning. ( − 3 , 0 , 0 ) , ( 0 , 0 , 0 ) , ( 1 , 2 , 3 )

To determine
Whether the vertices given as, (3,0,0),(0,0,0),(1,2,3) make an acute triangle, an obtuse triangle, or a right triangle.

Explanation

Let, the vertices be denoted as A=(3,0,0),B=(0,0,0),C=(1,2,3).

Let, the angle between AB and AC be α, and between BA and BC be β and the third angle of the triangle be γ,

So,

γ=π(α+β).

Vectors, AB=3,0,0, BA=3,0,0, AC=4,2,3 and BC=1,2,3.

Find the angles as;

u.v=uvcosθ,cosθ=u.vuvθ=arccos(u.vuv)

So,

u=u

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