# Find vector $$\vec{b}$$, if $$\vec{a}+\vec{b}$$+$$\vec{c}$$=8$$\hat{i}$$+2$$\hat{j}$$ where $$\vec{a}$$=$$\hat{i}$$-6$$\hat{j}$$ and $$\vec{c}$$=3$$\hat{i}$$+7$$\hat{j}$$.

Category: QuestionsFind vector $$\vec{b}$$, if $$\vec{a}+\vec{b}$$+$$\vec{c}$$=8$$\hat{i}$$+2$$\hat{j}$$ where $$\vec{a}$$=$$\hat{i}$$-6$$\hat{j}$$ and $$\vec{c}$$=3$$\hat{i}$$+7$$\hat{j}$$.
Editor">Editor Staff asked 11 months ago

Find vector \vec{b}, if \vec{a}+\vec{b}+\vec{c}=8\hat{i}+2\hat{j} where \vec{a}=\hat{i}-6\hat{j} and \vec{c}=3\hat{i}+7\hat{j}.

(a) 4\hat{i}+4\hat{j}

(b) \hat{i}+4\hat{j}

(c) 4\hat{i}–\hat{j}

(d) 4\hat{i}+\hat{j}

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Editor">Editor Staff answered 11 months ago

Right choice is (d) 4\hat{i}+\hat{j}

To elaborate: Given that, \vec{a}+\vec{b}+\vec{c}=8\hat{i}+2\hat{j} -(1)

Given: \vec{a}=\hat{i}-6\hat{j} and \vec{c}=3\hat{i}+7\hat{j}

Substituting the values of \vec{a} and \vec{b} in equation (1), we get

\vec{a}+\vec{b}+\vec{c}=8\hat{i}+2\hat{j}

(\hat{i}-6\hat{j})+\vec{b}+(3\hat{i}+7\hat{j})=8\hat{i}+2\hat{j}

∴\vec{c}=(8\hat{i}+2\hat{j})-(\hat{i}-6\hat{j})-(3\hat{i}+7\hat{j})

=(8-1-3) \hat{i}+(2+6-7) \hat{j}

=4\hat{i}+\hat{j}