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Chapter 10: Q. 58 (page 802)

Prove part (b) of Theorem 10.8 for vectors in R3; that is, show that for u=(u1,u2,u3),v=(v1,v2,v3)andw=(w1,w2,w3),role="math" localid="1663642720955" (u+v)+w=u+(v+w).

Short Answer

Expert verified

It is proved that(u+v)+w=u+(v+w).

Step by step solution

01

Consider vectors in R3

Let us consider,

u=i+j+kv=i-j-kw=2i+2j+k

02

Find LHS and RHS

LHS=(u+v)+w=(i+j+k+i-j-k)+(2i+2j+k)=(2i)+(2i+2j+k)=4i+2j+kRHS=u+(v+w)=(i+j+k)+(i-j-k+2i+2j+k)=(i+j+k)+(3i+j)=4i+2j+kHere,LHS=RHS

Hence, proved.

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