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