Question

find the unit vector in the same direction as$v$

$v=-5i+12j$

Short answer

The unit vector in the direction of the vector$v=-5i+12j$is$v=-\frac{5}{13}i+\frac{12}{13}j$.

Step-by-step solution

Step 1. Given data

The given vector is

$v=-5i+12j$

Step 2. Finding the magnitude

The magnitude of the vector $v=-5i+12j$is

$$\begin{gathered} \left|v\right|=\sqrt{{(-5)}^2+{\left(12\right)}^2} \\ \Rightarrow \left|v\right|=\sqrt{25+144} \\ \Rightarrow \left|v\right|=\sqrt{169} \\ \Rightarrow \left|v\right|=13 \end{gathered}$$

Step 3. Finding the unit vector

The unit vector $u$in the direction of is:

Substitute the values of vector and magnitude vector in the formula.

$$\begin{gathered} u=\frac{-5i+12j}{\left|13\right|} \\ \Rightarrow u=\frac{-5}{13}i+\frac{12}{13}j \end{gathered}$$