Given a⃗=5i^−2j^,b⃗=3i^+3j^ and c⃗=4i^−j^\vec{a}=5\hat{i}-2\hat{j}, \vec{b}=3\hat{i}+3\hat{j} \ and \ \vec{c}=4\hat{i}-\hat{j}a=5i^−2j^,b=3i^+3j^ and c=4i^−j^.
⟹ a⃗−b⃗−c⃗=(5i^−2j^)−(3i^+3j^)−(4i^−j^) =5i^−2j^−3i^−3j^−4i^+j^=(5−3−4)i^+(−2−3+1)j^ =−2i^−4j^\implies \vec{a}-\vec{b}-\vec{c}=(5\hat{i}-2\hat{j})-(3\hat{i}+3\hat{j})-(4\hat{i}-\hat{j}) \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 5\hat{i}-2\hat{j}-3\hat{i}-3\hat{j}-4\hat{i}+\hat{j} = (5-3-4)\hat{i} +(-2-3+1)\hat{j} \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = -2 \hat{i} - 4 \hat{j}⟹a−b−c=(5i^−2j^)−(3i^+3j^)−(4i^−j^) =5i^−2j^−3i^−3j^−4i^+j^=(5−3−4)i^+(−2−3+1)j^ =−2i^−4j^
So, a⃗−b⃗−c⃗=−2i^−4j^\vec{a}-\vec{b}-\vec{c}= -2 \hat{i} - 4\hat{j}a−b−c=−2i^−4j^ .
