If \(\vec{a}\)=\(\hat{i}\)+4\(\hat{j}\) and \(\vec{b}\)=3\(\hat{i}\)-3\(\hat{j}\). Find the magnitude of \(\vec{a}+\vec{b}\).

Category: QuestionsIf \(\vec{a}\)=\(\hat{i}\)+4\(\hat{j}\) and \(\vec{b}\)=3\(\hat{i}\)-3\(\hat{j}\). Find the magnitude of \(\vec{a}+\vec{b}\).
Editor">Editor Staff asked 11 months ago

If \(\vec{a}\)=\(\hat{i}\)+4\(\hat{j}\) and \(\vec{b}\)=3\(\hat{i}\)-3\(\hat{j}\). Find the magnitude of \(\vec{a}+\vec{b}\).
 
(a) \(\sqrt{6}\)
 
(b) \(\sqrt{11}\)
 
(c) \(\sqrt{5}\)
 
(d) \(\sqrt{17}\)
 
I had been asked this question in homework.
 
My question 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

The correct choice is (d) \(\sqrt{17}\)
 
Explanation: Given that, \(\vec{a}\)=\(\hat{i}\)+4\(\hat{j}\) and \(\vec{b}\)=3\(\hat{i}\)-3\(\hat{j}\)
 
∴\(\vec{a}+\vec{b}\)=(1+3) \(\hat{i}\)+(4-3) \(\hat{j}\)
 
=4\(\hat{i}\)+\(\hat{j}\)
 
|\(\vec{a}+\vec{b}\)|=\(\sqrt{4^2+1^2}=\sqrt{16+1}=\sqrt{17}\)