Thank you for reporting, we will resolve it shortly
Q.
The component of $\hat{i}$ in the direction of the vector $\hat{i} + \hat{j} +2\hat{k}$ is
Vector Algebra
Solution:
Unit vector along $\hat{i} + \hat{j} +2\hat{k}$ is $\frac{\hat{i} + \hat{j} +2\hat{k}}{\sqrt{6}}$
Hence, the component of $\hat{i}$ along the given vector,
$=$ Projection of $\hat{i}$ on $\frac{\hat{i} + \hat{j} +2\hat{k}}{\sqrt{6}}$
$= \hat{i}\cdot\frac{\left(\hat{i} + \hat{j} +2\hat{k}\right)}{\sqrt{6}} = \frac{1}{\sqrt{6}}$
$= \frac{\sqrt{6}}{6}$