Question

For v= -5i - 2j, find unit vector u in the direction of v, and write your answer as a linear combination of the standard unit vectors i and j.

Answer 1

Answer: Third option

`u = -(5√(29))/(29)i -(2√(29))/(29)j`

Explanation:

A unit vector
`u` is a vector that has magnitude 1.

To find a unit vector in the direction of the vector v we must first calculate the magnitude of v and then divide the vector v by its magnitude

The vector v is:

v = -5i - 2j

The magnitude of the vector is:

`| v | =√((-5)^2 +(-2)^2)\\\\|v|= √(29)`

Now we divide the vector v by its magnitude

`u = (1)/(√(29))v`

`u = -(5)/(√(29))i -(2)/(√(29))j`

Simplifying we have to

`u = -(5√(29))/(29)i -(2√(29))/(29)j`