Answer
$\vec{a} =9\hat{i}+12\hat{j}$
Work Step by Step
Given vectors:
$\vec{a}-\vec{b}=2\vec{c}$
$\vec{a}+\vec{b}=4\vec{c}$
$\vec{c}=3\hat{i}+4\hat{j}$
Now substitute $\vec {c}$ value in above two equations:
$\vec{a}-\vec{b}=2(3\hat{i}+4\hat{j}) $
$\vec{a}-\vec{b}=6\hat{i}+8\hat{j}..............equation\ (1)$
and
$\vec{a}+\vec{b}=4(3\hat{i}+4\hat{j})$
$\vec{a}+\vec{b}=12\hat{i}+16\hat{j}................equation (2)$
Add equation (1) and equation (2);
$\vec{a}-\vec{b}+\vec{a}+\vec{b} =6\hat{i}+8\hat{j}+12\hat{i}+16\hat{j} $
$2\vec{a} =18\hat{i}+24\hat{j}$
$\vec{a} =9\hat{i}+12\hat{j}$
