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 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

If the perimeter, p of a rectangle with length l and width w is given by the equation p=2l+2w , then

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 .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

The perimeter p of a rectangle of sides l and b is given by P=2(l+b) .Here,2 is a constant and l and b are variables.

Let vec a and vec b be two unit vectors such that |vec a+vec b|=sqrt(3) if vec c=vec a+2vec b+3(vec aXvec b) then 2|vec c| is equal to

If vec a and vec b are unit vectorts,then the greatest value fo 3|vec a+vec b|+|vec a-vec b| is 2 b.2sqrt(2)c.4d .none of these

If lines l_(1), l_(2) and l_(3) pass through a point P, then they are called…………. Lines.