Question

How do you find the unit vector in the direction of the given vector of w=7j−3i?

Answer 1

To find the unit vector in the same direction as a vector, we divide it by its magnitude. 

The magnitude of v⃗  is |v⃗ |=32+62+12−−−−−−−−−−√=46−−√.

We divide vector v⃗  by its magnitude to get the unit vector u⃗ v:

u⃗ v=v⃗ |v⃗ |=146−−√⋅[3,6,1] 

or 

u⃗ v=[346−−√,646−−√,146−−√]

All unit vectors have a magnitude of 1, so to verify we are correct:

|u⃗ v|=(346−−√)2+(646−−√