Find the value of x for which \[x \left( \hat{i} + \hat{j} + \hat{k} \right)\] is a unit vector.

We have, \[x \left( \hat{i} + \hat{j} + \hat{k} \right)\] is a unit vector.\[\therefore \sqrt{x^2 + x^2 + x^2} = 1\]\[ \Rightarrow \sqrt{3}\left| x \right| = 1\]\[ \Rightarrow \left| x \right| = \frac{1}{\sqrt{3}}\]\[ \Rightarrow x = \pm \frac{1}{\sqrt{3}}\]

Find the Value of X for Which X ( ^ I + ^ J + ^ K ) is a Unit Vector. - Mathematics

प्रश्न

Find the value of x for which $x (\hat{i} + \hat{j} + \hat{k})$ is a unit vector.

उत्तर

We have, $x (\hat{i} + \hat{j} + \hat{k})$ is a unit vector.
$∴ \sqrt{x^{2} + x^{2} + x^{2}} = 1$
$\Rightarrow \sqrt{3} | x | = 1$
$\Rightarrow | x | = \frac{1}{\sqrt{3}}$
$\Rightarrow x = \pm \frac{1}{\sqrt{3}}$

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Basic Concepts of Vector Algebra

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Q 15 Q 14 Q 16

पाठ 23: Algebra of Vectors - Exercise 23.6 [पृष्ठ ४९]

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पाठ 23 Algebra of Vectors
Exercise 23.6 | Q 15 | पृष्ठ ४९

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Find the Value of X for Which X ( ^ I + ^ J + ^ K ) is a Unit Vector. - Mathematics

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