The value of x if x(hat{i}+hat{j}+hat{k}) is | vedclass

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Question

(A) Given that the vector $x(\hat{i}+\hat{j}+\hat{k})$ is a unit vector,its magnitude must be equal to $1$.So,$|x(\hat{i}+\hat{j}+\hat{k})| = 1$.Using

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$ \pm \frac{1}{\sqrt{3}} $

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(A) Given that the vector $x(\hat{i}+\hat{j}+\hat{k})$ is a unit vector,its magnitude must be equal to $1$.So,$|x(\hat{i}+\hat{j}+\hat{k})| = 1$.Using the property $|k\vec{a}| = |k| |\vec{a}|$,we get:$|x| |\hat{i}+\hat{j}+\hat{k}| = 1$.The magnitude of the vector $(\hat{i}+\hat{j}+\hat{k})$ is $\sqrt{1^2 + 1^2 + 1^2} = \sqrt{3}$.Substituting this value,we have $|x| \sqrt{3} = 1$.Therefore,$|x| = \frac{1}{\sqrt{3}}$,which implies $x = \pm \frac{1}{\sqrt{3}}$.

The value of $x$ if $x(\hat{i}+\hat{j}+\hat{k})$ is a unit vector is:

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