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Question

If a=^i+^j+^k; b=^i^j+^k; c=^i+^j^k, then

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Solution

For a=i+j+k;b=ij+k;c=i+jk
A) ab+bc+ca=(1)+(1)+(1)=1
B) ((ac)c+(cb)a)b=((1)c+(1)a)b=(cb)b=cbbb=(1)1=2
C) (a+2b)(a+(ac)b)=(a+2b)(a+b)=aa+2bb+ab+a2b=3+2+1+2=8
D) (a+b)(a+b+c)=aa+ab+ac+ba+bb+bc=3+1+1+1+11=6

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