   Chapter 12.2, Problem 49E

Chapter
Section
Textbook Problem

# Figure 16 gives a geometric demonstration of Property 2 of vectors. Use components to give an algebraic proof of this fact for the case n = 2.

To determine

To prove: Algebraic proof of property 2 as a+(b+c)=(a+b)+c.

Explanation

Given:

The value of n as 2.

Formula used:

Consider two two-dimensional vectors such as a=a1,a2 and b=b1,b2.

Sum of vectors:

The vector sum of two vectors (a+b) is,

a+b=a1,a2+b1,b2=a1+b1,a2+b2

The property 2 is basically an associative law.

From Figure 16, write the expression for property 2.

a+(b+c)=(a+b)+c (1)

Here,

a, b, and c are vectors.

The value of n is 2, hence vectors are two-dimensional. Consider the vectors as a=a1,a2, b=b1,b2, and c=c1,c2

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