If `P` is any arbitrary point on the circumcircle of the equilateral triangle of side length `l` units, then `| vec P A|^2+| vec P B|^2+| vec P C|^2` is always equal to `2l^2` b. `2sqrt(3)l^2` c. `l^2` d. `3l^2`

If P is any arbitrary point on the circumcirlce of the equllateral trangle of side length l units, then | vec P A|^2+| vec P B|^2+| vec P C|^2 is always equal to 2l^2 b. 2sqrt(3)l^2 c. l^2 d. 3l^2

If D is the mid-point of the side B C of a triangle A B C , prove that vec A B+ vec A C=2 vec A Ddot

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 vec a ,\ vec b ,\ vec c are any time mutually perpendicular vectors of equal magnitude a , then | vec a+ vec b+ vec c| is equal to a b. sqrt(2)a c. sqrt(3)a d. 2a e. none of these

vec a , vec b , vec c are three coplanar unit vectors such that vec a+ vec b+ vec c=0. If three vectors vec p , vec q ,a n d vec r are parallel to vec a , vec b ,a n d vec c , respectively, and have integral but different magnitudes, then among the following options, | vec p+ vec q+ vec r| can take a value equal to a. 1 b. 0 c. sqrt(3) d. 2

In triangle A B C ,/_A=60^0,/_B=40^0,a n d/_C=80^0dot If P is the center of the circumcircle of triangle A B C with radius unity, then the radius of the circumcircle of triangle B P C is (a) 1 (b) sqrt(3) (c) 2 (d) sqrt(3) 2

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

The perimeter P of a rectangle of sides l\ a n d\ b is given by P=2\ (l+b)dot\ evaluate the variable and constant part

If vec a , vec ba n d vec c are unit coplanar vectors, then the scalar triple product [2 vec a- vec b2 vec b- vec c2 vec c- vec a] is 0 b. 1 c. -sqrt(3) d. sqrt(3)

Show that the distance d from point P to the line l having equation vec r= vec a+lambda vec b is given by d=(| vec bxx vec P Q|)/(| vec s|),w h e r eQ is any point on the line ldot