A) i ? j + k
B) 2i ? 2j
C) 3i ? j + k
D) 2i + 2j ? k
Correct Answer: B
Solution :
\[\because \,\,a\times (b\times c)=(a.c)b-(a.b)c\] \[\because \,\,a.c=(i+j-k)\,.\,(i-j-k)=1-1+1=1\] \[a.b=(i+j-k)\,.\,(i-j+k)=1-1-1=-1\] \\[a\times (b\times c)=(1)b-(-1)\,\mathbf{c}\] \[=\mathbf{b}+\mathbf{c}=\mathbf{i}-\mathbf{j}+\mathbf{k}+\mathbf{i}-\mathbf{j}-\mathbf{k}\]\[=2\mathbf{i}-2\mathbf{j}\].
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