Answer
$\vec{b}=3\hat{i}+4\hat{j}$
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
$\vec{a}+\vec{b}=4(3\hat{i}+4\hat{j})$
$\vec{a}+\vec{b}=12\hat{i}+16\hat{j}............equation (2)$
Subtract 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}) $
$-2\vec{b} = -6\hat{i}-8\hat{j}$
$\vec{b}=3\hat{i}+4\hat{j}$
