Question

What is the unit vector of this vector v = -2i + 5j?

Answer 1

`color(blue)(vec(u)=-2/sqrt(29)i+5/sqrt(29)j)` is a unit vector with the same direction as `vec(v)=-2+5j`

Explanation:

The unit vector, `vec(u)` corresponding to a given vector `vec(v)` can be calculated by dividing the terms of `vec(v)` by the magnitude (length) of `vec(v)`

`color(white)("XXX")vec(u)=vec(v)/abs(vec(v))`

`abs(vec(v))` is calculated using the Pythagorean Theorem.
In this case with `vec(v)=-2i+5j`
`color(white)("XXX")abs(vec(v))=sqrt((-2)^2+5^2)=sqrt(29)`