If \(\vec{a}\)=9\(\hat{i}\)-2\(\hat{j}\)+7\(\hat{k}\), \(\vec{b}\)=5\(\hat{i}\)+\(\hat{j}\)-3\(\hat{k}\), find \(\vec{a}+\vec{b}\).

Category: QuestionsIf \(\vec{a}\)=9\(\hat{i}\)-2\(\hat{j}\)+7\(\hat{k}\), \(\vec{b}\)=5\(\hat{i}\)+\(\hat{j}\)-3\(\hat{k}\), find \(\vec{a}+\vec{b}\).
Editor">Editor Staff asked 11 months ago

If \vec{a}=9\hat{i}-2\hat{j}+7\hat{k}, \vec{b}=5\hat{i}+\hat{j}-3\hat{k}, find \vec{a}+\vec{b}.
 
(a) \hat{i}–\hat{j}+4\hat{k}
 
(b) 14\hat{i}–\hat{j}+4\hat{k}
 
(c) 14\hat{i}-3\hat{j}+4\hat{k}
 
(d) 14\hat{i}–\hat{j}+9\hat{k}
 
I had been asked this question in final exam.
 
This intriguing question comes from Addition of Vectors in division Vector Algebra of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
Interview Questions and Answers, Database Interview Questions and Answers for Freshers and Experience

1 Answers
Editor">Editor Staff answered 11 months ago

The correct choice is (b) 14\hat{i}–\hat{j}+4\hat{k}
 
The best I can explain: Given that, \vec{a}=9\hat{i}-2\hat{j}+7\hat{k}, \vec{b}=5\hat{i}+\hat{j}-3\hat{k}
 
We have to find \vec{a}+\vec{b}
 
∴\vec{a}+\vec{b}=(9\hat{i}-2\hat{j}+7\hat{k})+(5\hat{i}+\hat{j}-3\hat{k})
 
=(9+5) \hat{i}+(-2+1) \hat{j}+(7-3)\hat{k}
 
=14\hat{i}–\hat{j}+4\hat{k}