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Chapter 10: Q. 59 (page 802)

Prove part (c) of Theorem 10.8 for vectors in R3; that is, show that for u=(u1,u2,u3),v=(v1,v2,v3) and scalar c, role="math" localid="1663642684144" c(u+v)=cu+cv.

Short Answer

Expert verified

It is proved that,c(u+v)=cu+cv.

Step by step solution

01

Consider vectors

Let us consider vectors are,

u=2i+j+kv=i+3j+5kandc=2

02

Proof

Consider the LHS of the given expression,

LHS=c(u+v)=2(2i+j+k+i+3j+5k)=2(3i+4j+6k)=6i+8j+12k

RHS=cu+cv=2(2i+j+k)+2(i+3j+5k)=4i+2j+2k+2i+6j+10k=6i+8j+12k

It is observed that, LHS=RHS

Hence, proved.

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