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Chapter 10: Q. 57 (page 801)

Prove part (a) of Theorem 10.8 for vectors in R3; that is, show that for u=u1,u2,u3 and v=v1,v2,v3, u+v=v+u

Short Answer

Expert verified

It is proven thatu+v=v+u

Step by step solution

01

Given

VectorsuandvinR3.

02

Proof

Let us take two vectors,

u=1i+2j+3kandv=4i+5j+6kLHS=u+v=1i+2j+3k+4i+5j+6k=1i+4i+(2j+5j)+(3k+6k)=5i+7j+9kRHS=v+u=4i+5j+6k+1i+2j+3k=1i+4i+(2j+5j)+(3k+6k)=5i+7j+9k

It is observed that, LHS=RHS

Hence, proved.

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