If A, B and C are the vertices of a ΔABC, then what is the value of vector AB + BC + CA ?

Solution:

Consider ΔABC as the given triangle

Using the law of vector addition,

AB + BC = AC

Add CA on both sides

AB + BC + CA = CA + AC

We know that AC = - CA

So we get

AB + BC + CA = CA - CA

AB + BC + CA = 0

Therefore, the value of vector AB + BC + CA is 0.

If A, B and C are the vertices of a ΔABC, then what is the value of vector AB + BC + CA ?

Summary:

If A, B and C are the vertices of a ΔABC, then the value of vector AB + BC + CA is 0.