If \vec{a}=3\hat{i}+2\hat{j}+2\hat{k}, \vec{b}=2\hat{i}-8\hat{j}+\hat{k}, find \vec{a}+\vec{b}.

Category: QuestionsIf \vec{a}=3\hat{i}+2\hat{j}+2\hat{k}, \vec{b}=2\hat{i}-8\hat{j}+\hat{k}, find \vec{a}+\vec{b}.
Editor">Editor Staff asked 11 months ago

If \vec{a}=3\hat{i}+2\hat{j}+2\hat{k}, \vec{b}=2\hat{i}-8\hat{j}+\hat{k}, find \vec{a}+\vec{b}.
 
(a) 5\hat{i}+\hat{j}+3\hat{k}
 
(b) 5\hat{i}-6\hat{j}+3\hat{k}
 
(c) 5\hat{i}-6\hat{j}-3\hat{k}
 
(d) 5\hat{i}+6\hat{j}+3\hat{k}
 
The question was posed to me in a national level competition.
 
My doubt is from Addition of Vectors topic in portion Vector Algebra of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

Right choice is (b) 5\hat{i}-6\hat{j}+3\hat{k}
 
The best I can explain: It is given that, \vec{a}=3\hat{i}+2\hat{j}+2\hat{k}, \vec{b}=2\hat{i}-8\hat{j}+\hat{k}
 
To find: \vec{a}+\vec{b}
 
∴\vec{a}+\vec{b}=(3\hat{i}+2\hat{j}+2\hat{k})+(2\hat{i}-8\hat{j}+\hat{k})
 
=(3+2) \hat{i}+(2-8) \hat{j}+(2+1)\hat{k}
 
=5\hat{i}-6\hat{j}+3\hat{k}