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

If in a right-angled triangle A B C , the hypotenuse A B=p ,then vec(AB).vec(AC)+ vec(BC). vec(BA)+ vec(CA).vec(CB) is equal to 2p^2 b. (p^2)/2 c. p^2 d. none of these

If in a right-angled triangle A B C , the hypotenuse A B=p ,then vec(AB).vec(AC)+ vec(BC). vec(BA)+ vec(CA).vec(CB) is equal to 2p^2 b. (p^2)/2 c. p^2 d. none of these

If in a right-angled triangle A B C , the hypotenuse A B=p ,then vec(AB).vec(AC)+ vec(BC). vec(BA)+ vec(CA).vec(CB) is equal to 2p^2 b. (p^2)/2 c. p^2 d. none of these

If in a right-angled triangle ABC, the hypotenuse AB=p, then vec AB.AC+vec BC*vec BA+vec CA.vec CB is equal to 2p^(2) b.(p^(2))/(2) c.p^(2) d.none of these

A , B , C , D are any four points, prove that vec A B dot vec C D+ vec B Cdot vec A D+ vec C Adot vec B D=0.

A , B , C , D are any four points, prove that vec A Bdot vec C D+ vec B Cdot vec A D+ vec C Adot vec B D=4(Area \ of triangle ABC).

A , B , C , D are any four points, prove that vec A Bdot vec C D+ vec B Cdot vec A D+ vec C Adot vec B D=4(Area \ of triangle ABC).

If a ,\ b ,\ c are non coplanar vectors then ( vec adot( vec bxx vec c))/(( vec cxx vec a)dot vec b)+( vec bdot( vec axx vec c))/( vec cdot( vec axx vec b)) is equal to 2 b. "\ "0"\ " c. 1 d. none of these

If vec adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then

In a regular hexagon A B C D E F ,\ A vec B=a ,\ B vec C= vec b\ a n d\ vec C D=c\ T h e n\ vec A E=