Find the value of x for which x-k- is a unit vector-

Given, x(î+ĵ+k̂) is a unit vector, therefore |x(î+ĵ+k̂)|=1 ⇒ |xî+xĵ+xk̂|=1⇒√(x^2+x^2+x^2)=1 ⇒√(3x^2)=1⇒±√(3)x=1⇒ x=±1/√(3) Hence, the required values of x are ...

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Standard XII

Physics

Vector Notation

Find the valu...

Question

Find the value of x for which $x (^i +^j +^k)$ is a unit vector.

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Solution

Given, $x (^i +^j +^k)$ is a unit vector, therefore $| x (^i +^j +^k) | = 1$
$\Rightarrow | x^i + x^j + x^k | = 1 \Rightarrow \sqrt{x^{2} + x^{2} + x^{2}} = 1$
$\Rightarrow \sqrt{3 x^{2}} = 1 \Rightarrow \pm \sqrt{3} x = 1 \Rightarrow x = \pm \frac{1}{\sqrt{3}}$
Hence, the required values of x are $\pm \frac{1}{\sqrt{3}}$ .

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Find the value of x for which x(^i+^j+^k) is a unit vector.

Given, x(^i+^j+^k) is a unit vector, therefore |x(^i+^j+^k)|=1 ⇒|x^i+x^j+x^k|=1⇒√x2+x2+x2=1 ⇒√3x2=1⇒±√3x=1⇒x=±1√3 Hence, the required values of x are ±1√3.

Find the value of x for which $x (^i +^j +^k)$ is a unit vector.