Find the magnitude of \vec{a}+\vec{b}, if \vec{a}=4\hat{i}+9\hat{j} and \vec{b}=6\hat{i}.

Category: QuestionsFind the magnitude of \vec{a}+\vec{b}, if \vec{a}=4\hat{i}+9\hat{j} and \vec{b}=6\hat{i}.
Editor">Editor Staff asked 11 months ago

Find the magnitude of \vec{a}+\vec{b}, if \vec{a}=4\hat{i}+9\hat{j} and \vec{b}=6\hat{i}.
 
(a) \sqrt{181}
 
(b) \sqrt{81}
 
(c) \sqrt{11}
 
(d) \sqrt{60}
 
This question was addressed to me in final exam.
 
The query is from Addition of Vectors topic in section 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

Correct answer is (a) \sqrt{181}
 
To explain I would say: Given that, \vec{a}=4\hat{i}+9\hat{j} and \vec{b}=6\hat{i}
 
∴\vec{a}+\vec{b}=(4+6) \hat{i}+9\hat{j}
 
=10\hat{i}+9\hat{j}
 
|\vec{a}+\vec{b}|=\sqrt{10^2+9^2}=\sqrt{100+81}=\sqrt{181}