Question

In Problems 45–50, find the unit vector in the same direction as v.

$v=5i$

Short answer

The unit vector in the same direction as $v=5i$is $i$

Step-by-step solution

Step 1. Given

The vector $v=5i$

To find the unit vector.

Step 2. Unit vector in the direction of v

For any nonzero vector v, the vector $u=\frac{v}{||v||}$ is a unit vector that has the same direction as $v$.

Step 3. Find v

Now,

$$\begin{gathered} ||v||=||5i|| \\ =\sqrt{5^2} \\ =5 \end{gathered}$$

Step 4. Find the unit vector.

The unit vector,

$$\begin{gathered} u=\frac{v}{||v||} \\ =\frac{5i}{5} \\ =i \end{gathered}$$