If in a right-angled triangle `A B C ,` the hypotenuse `A B=p ,t h e n vec A BdotA C+ vec B Cdot vec B A+ vec C Adot vec C B` is equal to `2p^2` b. `(p^2)/2` c. `p^2` d. none of these

Options

A. `2p^(2)`
B. `p^(2)/2`
C. `p^(2)`
D. none of these

Answer

c

Explanation

we have
` vec(AB). Vec(AC) + vec(BC) + vec(BA) + vec(CA) . Vec(CB)`
` AB ( AC cos theta + BC sin theta)`
` AB ( AC cos theta + BC sin theta)`
`AB (((AC)^(2))/(AB)) + ((BC)^(2))/(AB)`
` AC^(2) + BC^(2) = AB^(2) + p^(2)`