Question #120515

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 ?

Expert's answer

**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{\u0421}" :

"|\\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.

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