Question

Given u = <3, -4>, we can find a unit vector in the direction of u by:

Answer 1

To find a unit vector in the direction of a vector given we just need to divide it by its magnitude, that is:

`\mathbf{\hat{u}}=\frac{\mathbf{u}}{\lvert{\mathbf{u}}\rvert}`

The magnitude of a vector is given by:

`\lvert{\mathbf{u}}\rvert=√(u_x^2+u_y^2)`

In this case we have:

`\lvert{\mathbf{u}}\rvert=√(3^2+(-4)^2)=√(25)=5`

Hence the magnitude of the vector given is 5. Now that we know the magnitude of the vector we need to divide it by this. Therefore, to find a unit vector we multiply u by 1/5