If in a right-angled triangle ABC, the hypotenuse AB = p , then `vec(AB).vec(AC)+vec(BC).vec(BA)+vec(CA).vec(CB)`is equal to

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)`