Question

May someone please explain how to find the magnitude \[||v|| \] and direction angle \[\theta\] , to the nearest tenth of a degree, for the given vector v? \[v = -4i - 3j\
I'm not sure how to solve this...thank you.

Answer 1

<v = -4i - 3j> => <-4, -3>

-4 -3
x y

starting from the origin, since we don't have a starting point given I assume you should be able to see the "adjacent side" and the "opposite side" of that reference angle, and thus you can get the angle

as far as the magnitude, the magnitude of it, or ||v|| is really how long it

recall that \(\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ -4}}\quad ,&{\color{blue}{ -3}})\quad &({\color{red}{ 0}}\quad ,&{\color{blue}{ 0}})
\end{array}\qquad
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}\)