Write two different vectors having same magnitude. - Mathematics

Question

Write two different vectors having same magnitude.

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Solution

Consider $\vec{a} = (\vec{i} - 2 \vec{j} + 3 \vec{k})$ and $\vec{b} = (2 \vec{i} + \vec{j} - 3 \vec{k})$ .

It can be observed that,

$| \vec{a} | = \sqrt{1^{2} + {(- 2)}^{2} + 3^{2}}$

$= \sqrt{1 + 4 + 9}$

$= \sqrt{14}$

and $| \vec{b} | = \sqrt{2^{2} + 1^{2} + {(- 3)}^{2}}$

$= \sqrt{4 + 1 + 9}$

$= \sqrt{14}$ .

Hence, $\vec{a} and \vec{b}$ are two different vectors with the same magnitude. The vectors are different because they have different directions.

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Multiplication of a Vector by a Scalar

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Q 2.Q 1.Q 3.

Chapter 10: Vector Algebra - Exercise 10.2 [Page 440]

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Chapter 10 Vector Algebra
Exercise 10.2 | Q 2. | Page 440

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Write two different vectors having same magnitude. - Mathematics

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