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Chapter 10: Q 35. (page 801)

Find the norm of the vector. $v = (\frac{1}{3}, \frac{1}{3}, - \frac{1}{3})$

Short Answer

Expert verified

The norm of the vector $v = (\frac{1}{3}, \frac{1}{3}, - \frac{1}{3})$ is $\sqrt{\frac{1}{3}}$ .

Step by step solution

Step 1. Given information .

We have given vector $v = (\frac{1}{3}, \frac{1}{3}, - \frac{1}{3})$ .

Step 2. Find the norm of the vector.

$||v|| = \sqrt{a^{2} + b^{2} + c^{2}} = \sqrt{{(\frac{1}{3})}^{2} + {(\frac{1}{3})}^{2} + {(\frac{1}{3})}^{2}} = \sqrt{\frac{1}{9} + \frac{1}{9} + \frac{1}{9}} = \sqrt{\frac{3}{9}} = \sqrt{\frac{1}{3}}$

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Step by step solution

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Find the norm of the vector. $v = (\frac{1}{3}, \frac{1}{3}, - \frac{1}{3})$