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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

A

`2p^(2)`

B

`p^(2)/2`

C

`p^(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
c
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)`
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