If $\vec a$ and $\vec b$ are two vectors such that $|\vec a| = 7$ and $|\vec b|=4$, then the value of scalar product of vectors $2\vec a-3\vec b$ and $2\vec a+3\vec b$ is

52

$|\vec a| = 7$ and $|\vec b|=4$

$\vec{v_1}=2\vec a-3\vec b$ and $\vec{v_2}=2\vec a+3\vec b$

$\vec{v_1}.\vec{v_2}=4|\vec a|^2-9|\vec b|^2$

$=4×7^2-9×4^2$

$=4(49)-9×16$

$=4(49-36)=4×13=52$