Q 37, - Calculus

Question

Find $||v||$ and find the unit vector in the direction of $v$.

$v = \left(3, -4\right)$

Step-by-Step Solution

Answer

The norm of the vector $v=\left(3,-4\right)$ is $5$ and the unit vector in the direction of $v=\left(3,-4\right)$ is $\frac{1}{5}\left(3,-4\right)$.

Step 1. Given information .

We have given vector $v=\left(3,-4\right)$.

Step 2. Find the norm of the vector and unit vector in the direction of v .

$$\begin{gathered} ||v||=\sqrt{a^2+b^2} \\ =\sqrt{3^2+{\left(-4\right)}^2} \\ =\sqrt{9+16} \\ =\sqrt{25} \\ =5 \end{gathered}$$

The unit vector in the direction of  $v$ is $\frac{1}{||v||}v$.

$\frac{1}{||v||}v=\frac{1}{5}\left(3,-4\right)$