1.

If in a right-angledtriangle `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 theseA. `2p^(2)`B. `p^(2)/2`C. `p^(2)`D. none of these

Answer» Correct Answer - 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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