$$\vec{a}$$=$$\hat{i}$$ + 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
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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.