Question

In a triangle $ABC$, if $|\overrightarrow{BC}|=3,|\overrightarrow{CA}|=5$ and $|\overrightarrow{BA}|=7,$ then the projection of the vector $\overrightarrow{BA}$ on $\overrightarrow{BC}$ is equal to:

• A. $\frac{13}{2}$
• B. $\frac{15}{2}$
• C. $\frac{11}{2}$
• D. $\frac{19}{2}$

Answer 1

The correct option is C $\frac{11}{2}$

Projection of $\overrightarrow{BA}\text{on}\overrightarrow{BC}$


$=\left|\frac{\overrightarrow{BA}.\overrightarrow{BC}}{|\overrightarrow{BC}|}\right|$

$=\frac{|\overrightarrow{BA}|.|\overrightarrow{BC}|\cos B}{|\overrightarrow{BC}|}$

$=7.\left(\frac{7^2+3^2-5^2}{2\times 7\times 3}\right)$

$=\frac{11}{2}\text{units}$