A) 11
B) 15
C) 18
D) 36
Correct Answer: A
Solution :
\[\mathbf{a}=(1,\,-1,\,2),\,\,\mathbf{b}=(-\,2,\,3,\,5),\,\mathbf{c}=(2,\,-2,\,4)\] So, \[\mathbf{a}=(1,-1,2)\equiv \mathbf{i}-\mathbf{j}+2\mathbf{k};\,\,\mathbf{b}=(-2,3,5)\equiv -\,2\mathbf{i}+3\mathbf{j}+5\mathbf{k}\] and \[\mathbf{c}=(2,-2,4)\equiv 2\mathbf{i}-2\mathbf{j}+4\mathbf{k}\] \[\Rightarrow \mathbf{a}-2\mathbf{b}+3\mathbf{c}=(\mathbf{i}-\mathbf{j}+2\mathbf{k})-2(-2\mathbf{i}+3\mathbf{j}+5\mathbf{k})\] \[+3(2\mathbf{i}-2\mathbf{j}+4\mathbf{k})\] \[=11\mathbf{i}-13\mathbf{j}+4\mathbf{k}\] and \[(\mathbf{a}-2\mathbf{b}+3\mathbf{c})\,.\,\mathbf{i}=11.\]
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