The unit vector in the direction of - - - -k- is be-

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Standard XII

Physics

Unit Vectors

The unit vect...

Question

The unit vector in the direction of $^i +^j +^k$ is be:

\frac{1}{\sqrt{3}} (^i +^j +^k)

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\sqrt{3} (^i +^j +^k)

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\frac{1}{\sqrt{2}} (^i +^j +^k)

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\sqrt{2} (^i +^j +^k)

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Solution

The correct option is A $\frac{1}{\sqrt{3}} (^i +^j +^k)$
A unit vector is given by dividing the vector by its magnitude, so that the resulting vector has magnitude 1 and is in the same direction as the original vector.
For the vector $(^i +^j +^k)$ , the unit vector would be given by $\frac{^i +^j +^k}{\sqrt{1 + 1 + 1}}$
$= \frac{^i +^j +^k}{\sqrt{3}}$

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The unit vector in the direction of ^i+^j+^k is be:

The correct option is A 1√3(^i+^j+^k)A unit vector is given by dividing the vector by its magnitude, so that the resulting vector has magnitude 1 and is in the same direction as the original vector.For the vector (^i+^j+^k), the unit vector would be given by ^i+^j+^k√1+1+1=^i+^j+^k√3

The unit vector in the direction of $^i +^j +^k$ is be: