Question

\(\vec{a}\)=\(\hat{i}\) + 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

Answer 1

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.