Answer to Question #120637 in Analytic Geometry for usman

Question

Determine \\(a-b-c\\), if \\(a=5i-2j\\), \\(b=3i+3j\\) and \\(c=4i-j\\)

Answer 1

Given $\vec{a}=5\hat{i}-2\hat{j}, \vec{b}=3\hat{i}+3\hat{j} \ and \ \vec{c}=4\hat{i}-\hat{j}$.

$\implies \vec{a}-\vec{b}-\vec{c}=(5\hat{i}-2\hat{j})-(3\hat{i}+3\hat{j})-(4\hat{i}-\hat{j}) \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 5\hat{i}-2\hat{j}-3\hat{i}-3\hat{j}-4\hat{i}+\hat{j} = (5-3-4)\hat{i} +(-2-3+1)\hat{j} \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = -2 \hat{i} - 4 \hat{j}$

So, $\vec{a}-\vec{b}-\vec{c}= -2 \hat{i} - 4\hat{j}$ .