How do you find a unit vector in the direction of the vector v=(-3,-4)?

Question

13503 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-06T17:10:52

$(-3/5,-4/5)$ .

The reqd. vector is in the direction of $vecv=(-3,-4)$ .

Therefore, it must be of the form

$k(-3,-4)=(-3k,-4k), where, k>0$

As this is a unit vector, $||((-3k,-4k))||=1$ .

$:. sqrt{(-3k)^2+(-4k)^2}=1$ .

$:. 5k=1 rArr k=+-1/5, but, k>0 rArr k!=-1/5. :. k=1/5$ .

Hence, the unit vector $=(-3/5,-4/5)$ .