Question

Which of these are unit vectors

• A. $\hat{i}$
• B. $\hat{i}+\hat{j}+\hat{k}$
• C. $\left(\frac{\hat{i}}{\sqrt{2}}\right)+\left(\frac{\hat{j}}{\sqrt{2}}\right)$
• D. $\left(\frac{4}{5}\right)\hat{i}+\left(\frac{3}{5}\right)\hat{j}$

Answer 1

Answer: (A), (C), (D)

$\left(\frac{4}{5}\right)\hat{i}+\left(\frac{3}{5}\right)\hat{j}$

Option a has just $\hat{i}$ so it's understood that it has magnitude 1 in x direction.

Option b is $\hat{i}+\hat{j}+\hat{k}$. Magnitude is found by $\sqrt{x^2+y^2+z^2}$

So we have magnitude as $\sqrt{1^2+1^2+1^2}=\sqrt{3}$so wrong.

Option c is $\frac{\hat{i}}{\sqrt{2}}+\frac{\hat{j}}{\sqrt{2}}$ so ,magnitude is $\sqrt{(\frac{1}{\sqrt{2}}{)}^2+(\frac{1}{\sqrt{2}}{)}^2}=1$so correct

Option d is $\frac{4}{5}\hat{i}+\frac{3}{5}\hat{j}$ so ,magnitude is $\sqrt{(\frac{4}{5}{)}^2+(\frac{3}{5}{)}^2}=1$so correct