   Chapter 11.2, Problem 97E

Chapter
Section
Textbook Problem

# Using a Triangle and Vectors Let A, B, and C be vertices of a triangle. Find A B ⇀ + B C ⇀ + C A ⇀ .

To determine

To calculate: The value of AB+BC+CA where A,B,C are vertices of a triangle.

Explanation

Given:

The vertices of a triangle are A,B,C.

Formula used:

The component form for any vector x directed by a line segment with end points P=(p1,p2,p3) and Q=(q1,q2,q3) is:

x=v1,v2,v3=q1p1,q2p2,q3p3

Addition of vectors x=a,b,c and y=m,n,o is:

z=a+m,b+n,c+o

Calculation:

The vertices of a triangle are A,B,C. Suppose the points are A=(a1,a2,a3), B=(b1,b2,b3) and C=(c1,c2,c3).

Since, the component form for any vector x directed by a line segment with end points P=(p1,p2,p3) and Q=(q1,q2,q3) is:

x=v1,v2,v3=q1p1,q2p2,q3p3

So AB,

AB=v1,v2,v3=b1a1,b2a2,b3a3

So BC

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