Find the sum of the vectors \vec{a}=6\hat{i}-3\hat{j} and \vec{b}=5\hat{i}+4\hat{j}.

Category: QuestionsFind the sum of the vectors \vec{a}=6\hat{i}-3\hat{j} and \vec{b}=5\hat{i}+4\hat{j}.
Editor">Editor Staff asked 11 months ago

Find the sum of the vectors \vec{a}=6\hat{i}-3\hat{j} and \vec{b}=5\hat{i}+4\hat{j}.
 
(a) 11\hat{i}+\hat{j}
 
(b) 11\hat{i}–\hat{j}
 
(c) -11\hat{i}+\hat{j}
 
(d) \hat{i}+\hat{j}
 
I had been asked this question in semester exam.
 
This question is from Addition of Vectors in section Vector Algebra of Mathematics – Class 12
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1 Answers
Editor">Editor Staff answered 11 months ago

Correct answer is (a) 11\hat{i}+\hat{j}
 
The explanation: Given that, \vec{a}=6\hat{i}-3\hat{j} and \vec{b}=5\hat{i}+4\hat{j}
 
The sum of the vectors is given by \vec{a}+\vec{b}.
 
∴\vec{a}+\vec{b}=(6\hat{i}-3\hat{i})+(5\hat{i}+4\hat{j})
 
=(6+5) \hat{i}+(-3+4)\hat{j}
 
=11\hat{i}+\hat{j}