Vector components, vector magnitudes and directions, vector addition, unit vectors The figure below shows a vector \vec{A} with magnitude 22.9 m and direction 158° (CCW from the $+x$ axis).
Using the graph, what sign (+ or -) would you expect each of the components to be?
$A_x$ sign:
$\bigcirc$ Positive
$\bigcirc$ 0
$\bigcirc$ Negative
$A_y$ sign:
$\bigcirc$ Positive
$\bigcirc$ 0
$\bigcirc$ Negative
Calculate the value of $A_x$. ____ m
Calculate the value of $A_y$. ____ m
The figure below shows a vector \vec{B} with magnitude 46.3 m and direction -150° (Positive is CCW from the $+x$ axis).
Using the graph, what sign (+ or -) would you expect each of the components to be?
$B_x$ sign:
$\bigcirc$ Positive
$\bigcirc$ 0
$\bigcirc$ Negative
$B_y$ sign:
$\bigcirc$ Negative
$\bigcirc$ 0
$\bigcirc$ Positive
Calculate the value of $B_x$. ____ m
Calculate the value of $B_y$. ____ m
The figure below shows the vectors \vec{A} and \vec{B} from above drawn head-to-tail.
Using the graph, what sign (+ or -) would you expect each of the components of the vector sum \vec{C} = \vec{A} + \vec{B} to be?
$C_x$ sign:
$\bigcirc$ 0
$\bigcirc$ Positive
$\bigcirc$ Negative
$C_y$ sign:
$\bigcirc$ Positive
$\bigcirc$ Negative
$\bigcirc$ 0
Calculate the value of $C_x$. ____ m
Calculate the value of $C_y$. ____ m
Calculate the magnitude $|\vec{C}|$. ____ m
Calculate the direction (angle) between the $+x$ axis and \vec{C}. Give an angle $\theta$ in degrees with $-180^\circ < \theta \le 180^\circ$. ____ $^\circ$
