A) \[12\hat{i}+14\hat{j}+12\hat{k}\]
B) \[13\hat{i}+17\hat{j}+12\hat{k}\]
C) \[12\hat{i}+16\hat{j}-3\hat{k}\]
D) \[15\hat{i}+13\hat{j}+4\hat{k}\]
Correct Answer: C
Solution :
Given, \[\vec{A}=3\hat{i}+\hat{j}+3\hat{k}\] \[\vec{B}=3\hat{i}+5\hat{j}-2\hat{k}\] Here, \[\vec{A}+3\vec{B}=\vec{C}\] \[(3\hat{i}+\hat{j}+3\hat{k})+3(3\hat{i}+5\hat{j}-2\hat{k})=\vec{C}\] \[\Rightarrow \] \[\vec{C}=12\hat{i}+16\hat{j}-3\hat{k}\]
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