Question

Find the unit vector in the direction of the vector \( \overrightarrow a = \hat i + \hat j + 2\hat k\) .

Answer 1

Hey There, 
To find the unit vector from a given vector, we Divide the Vector by its magnitude

Here, 
$\vec{a}=\hat{\imath}+\hat{\jmath}+2\hat{k} \\ \\ \textrm{Clearly, Magnitude is } \mid \vec{a} \mid = \sqrt{1^2+1^2+2^2} = \sqrt{6}$ 
Now, we just divide the vector by its magnitude, to find the unit vector. 
So,  $\hat{a} = \frac{\vec{a}}{\mid \vec{a} \mid} = \frac{\hat{\imath}+\hat{\jmath}+2\hat{k}}{\sqrt{6}} \\ \\ \implies \boxed{\hat{a}=\frac{1}{\sqrt{6}}\hat{\imath}+\frac{1}{\sqrt{6}}\hat{\jmath}+\frac{2}{\sqrt{6}}\hat{k}}$


Hope it helps
Purva
Brainly Community