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

Answer 1

Answer: (C)

Projection of $\overrightarrow{BA}$ on $\overrightarrow{BC}$ is equal to
$=|\overrightarrow{BA}|\cos \angle ABC$
$=7\left|\frac{7^2+3^2-5^2}{2\times 7\times 3}\right|=\frac{11}{2}$