The unit vector along - is-

The explanation for the correct answer: Option (C)Step 1: Calculating the unit vector along î+ĵ,we know R̂=⇀R/|R|R̂= It is the unit vector of ⇀R|R| is the magn ...

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Standard XII

Mathematics

Unit Vectors

The unit vect...

Question

The unit vector along $\hat{i} + \hat{j}$ is:

$\hat{k}$

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$\hat{i} + \hat{j}$

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$\frac{\hat{i} + \hat{j}}{\sqrt{2}}$

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$\frac{\hat{i} + \hat{j}}{2}$

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Solution

The correct option is C
$\frac{\hat{i} + \hat{j}}{\sqrt{2}}$

The explanation for the correct answer:-
Option (C)
Step 1: Calculating the unit vector along $\hat{i} + \hat{j}$ ,
we know $\hat{R} = \frac{\overset{⇀}{R}}{|R|}$
$\hat{R}$ = It is the unit vector of $\overset{⇀}{R}$
$|R|$ is the magnitude of $\overset{⇀}{R}$
$\overset{⇀}{R}$ = $\hat{i} + \hat{j}$
$|R| = \sqrt{1^{2} + 1^{2}}$ = $\sqrt{2}$
$\hat{R} = \frac{\overset{⇀}{R}}{|R|}$ = $\frac{1}{\sqrt{2}} \hat{i} + \frac{1}{\sqrt{2}} \hat{j}$ = $\frac{\hat{i} + \hat{j}}{\sqrt{2}}$
Hence, option C is the correct answer.

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The unit vector along i^+j^ is:

The correct option is C i^+j^2The explanation for the correct answer:-Option (C)Step 1: Calculating the unit vector along i^+j^,we know R^=R⇀RR^= It is the unit vector of R⇀R is the magnitude of R⇀R⇀=i^+j^R=12+12= 2R^=R⇀R=12i^+12j^=i^+j^2Hence, option C is the correct answer.

The unit vector along $\hat{i} + \hat{j}$ is: