Question

How do you find a unit vector parallel to another vector?

Answer 1

Definition of unit vector:

A vector is a quantity that has both magnitude, as well as direction. A vector that has a magnitude of $1$is called a unit vector.

A unit vector is represented by the symbol '$^$ ', which is called a cap or hat, such as $\hat{a}$

To find the unit vector in the same direction of another vector, we have to divide the vector by its magnitude.

i.e. $\hat{\mathbf{a}}\mathbf{}\mathbf{=}\frac{\stackrel{\mathbf{\rightharpoonup }}{\mathbf{a}}}{\mathbf{\left|}\mathbf{a}\mathbf{\right|}}$

Where $\left|a\right|$is for norm or magnitude of vector$\stackrel{\rightharpoonup }{a}$.

For example:

$\stackrel{\rightharpoonup }{a}=(3,6,1)$

$\Rightarrow \left|a\right|=\sqrt{3^2+6^2+1^2}=\sqrt{46}$

Therefore, the unit vector parallel to the vector $\stackrel{\rightharpoonup }{a}$is given by

$\hat{a}=\frac{\stackrel{\rightharpoonup }{a}}{\left|a\right|}=\left(\frac{3}{\sqrt{46}},\frac{6}{\sqrt{46}},\frac{1}{\sqrt{46}}\right)$