Find the value of \vec{a}+\vec{b}+\vec{c}, if \vec{a}=4\hat{i}-4\hat{j}, \vec{b}=-3\hat{i}+2k, \vec{c}=7\hat{j}-8\hat{k}.

Category: QuestionsFind the value of \vec{a}+\vec{b}+\vec{c}, if \vec{a}=4\hat{i}-4\hat{j}, \vec{b}=-3\hat{i}+2k, \vec{c}=7\hat{j}-8\hat{k}.
Editor">Editor Staff asked 11 months ago

Find the value of \vec{a}+\vec{b}+\vec{c}, if \vec{a}=4\hat{i}-4\hat{j}, \vec{b}=-3\hat{i}+2k, \vec{c}=7\hat{j}-8\hat{k}.
 
(a) \hat{i}-3\hat{j}
 
(b) \hat{i}+3\hat{j}-6\hat{k}
 
(c) \hat{i}+\hat{j}+6\hat{k}
 
(d) \hat{i}+6\hat{k}
 
I had been asked this question during an online exam.
 
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Editor">Editor Staff answered 11 months ago

The correct option is (b) \hat{i}+3\hat{j}-6\hat{k}
 
For explanation: Given that, \vec{a}=4\hat{i}-4\hat{j}, \vec{b}=-3\hat{i}+2k, \vec{c}=7\hat{j}-8\hat{k}
 
To find: \vec{a}+\vec{b}+\vec{c}
 
∴\vec{a}+\vec{b}+\vec{c}=(4\hat{i}-4\hat{j}) +(-3\hat{i}+2k) +(7\hat{j}-8\hat{k})
 
=(4-3) \hat{i}+(-4+7) \hat{j}+(2-8)\hat{k}
 
=\hat{i}+3\hat{j}-6\hat{k}