Question

Let v1=(3,5) and v2=(-4,7) Compute the unit vectors in the direction of |v1| and |v2|?

Answer 1

By definition, the unit vector of v = (a,b) is
$\hat{v} = \frac{\vec{v}}{|v|}$

Therefore,
The unit vector of v₁ = (3,5) in the direction of |v₁| s
 (3,5)/√[3² + 5²]
= (3,5)/√34

The unit vector of v₂ in the direction of |v₂| is
(-4,7)/√[(-4)² + 7²]
= (-4,7)/√65

Answer:
The unit vector of v₁ in the direction of |v₁} is $( \frac{3}{\sqrt{34}} , \frac{5}{\sqrt{34}} )$
The unit vector of v₂ in the directin of |v₂| is
$( \frac{-4}{\sqrt{65}} , \frac{7}{\sqrt{65}} )$