Answer to Question #120515 in Mechanics | Relativity for rouda h

Question

Vectors A and B are shown in the figure. Vector C is given by C = B - A. The magnitude of vector A is 16.0 units, and the magnitude of vector B is 7.00 units. What is the magnitude of vector C ?

Answer 1

Solution.

$\overrightarrow{C}=\overrightarrow{B}-\overrightarrow{A};$

$|\overrightarrow{A}|=16.0$ units;

$|\overrightarrow{B}|=7.00$ units;

From the triangle by cosine theory we find the length of the vector $\overrightarrow{С}$ :

$|\overrightarrow{C}|^2=|\overrightarrow{A}|^2+|\overrightarrow{B}|^2-2|\overrightarrow{A}||\overrightarrow{B}|cos\phi;$

$|\overrightarrow{C}|^2=16.0^2+7.00^2-2\sdot16.0\sdot7.00\sdot cos79^o=262.19$ ;

$|\overrightarrow{C}|=16.19$ units;

Answer:$|\overrightarrow{C}|=16.19$ units.