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}