\(\vec{a}\)=\(\hat{i}\) + 2\(\hat{j}\) and \(\vec{b}\)=2\(\hat{i}\) + \(\hat{j}\) , Is |\(\vec{a}\)| = |\(\vec{b}\)|?

Category: Questions\(\vec{a}\)=\(\hat{i}\) + 2\(\hat{j}\) and \(\vec{b}\)=2\(\hat{i}\) + \(\hat{j}\) , Is |\(\vec{a}\)| = |\(\vec{b}\)|?
Editor">Editor Staff asked 11 months ago

\(\vec{a}\)=\(\hat{i}\) + 2\(\hat{j}\) and \(\vec{b}\)=2\(\hat{i}\) + \(\hat{j}\) , Is |\(\vec{a}\)| = |\(\vec{b}\)|?
 
(a) Yes
 
(b) No
 
I have been asked this question in quiz.
 
This question is from Multiplication of a Vector by a Scalar in chapter 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) Yes
 
For explanation I would say: As we know that magnitude of vector is calculated by formula \(\sqrt{x^2+ y^2}\).
 
Therefore, |\(\vec{a}\)| = \(\sqrt{12} + 22 = \sqrt{5}\) and \(|\vec{b}| = \sqrt{22} + 12 = \sqrt{5}\), they are equal.