यदि समबाहु त्रिभुज की भुजा a तथा शीर्ष `(x_(1),y_(1)), (x_(2),y_(2))" एव "(x_(3),y_(3))` हो, तो सिद्ध कीजिये की `|{:(,x_(1),y_(1),2),(,x_(2),y_(2),2),(,x_(3),y_(3),2):}|^(2) =3a^(4)`

If the coordinates of the vertices of an equilateral triangle with sides of length a are (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) then |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|^2=(3a^(4))/4

If the coordinates of the vertices of an equilateral triangle with sides of length a are (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) then |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|^2=(3a^(4))/4

An equilateral triangle has each side to a. If the coordinates of its vertices are (x_(1), y_(1)), (x_(2), y_(2)) and (x_(3), y_(3)) then the square of the determinat |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|^2 equals

If (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) are the vertices of a triangle whose area is 'k' square units, then |(x_(1),y_(1),4),(x_(2),y_(2),4),(x_(3),y_(3),4)|^(2) is

An equilateral triangle has each side to a. If the coordinates of its vertices are (x_(1), y_(1)), (x_(2), y_(2)) and (x_(3), y_(3)) then the square of the determinat |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)| equals

An equilateral triangle has each side equal to a. If the coordinates of its vertices are (x_(1), y_(1)), (x_(2), y_(2)) and (x_(3), y_(3)) then the square of the determinant |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)| equals

An equilateral triangle has each side to a. If the coordinates of its vertices are (x_(1), y_(1)), (x_(2), y_(2)) and (x_(3), y_(3)) then the square of the determinat |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)| equals

STATEMENT-1: If three points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) are collinear, then |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|=0 STATEMENT-2: If |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|=0 then the points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) will be collinear. STATEMENT-3: If lines a_(1)x+b_(1)y+c_(1)=0,a_(2)=0and a_(3)x+b_(3)y+c_(3)=0 are concurrent then |{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|=0

STATEMENT-1: If three points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) are collinear, then |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|=0 STATEMENT-2: If |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|=0 then the points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) will be collinear. STATEMENT-3: If lines a_(1)x+b_(1)y+c_(1)=0,a_(2)=0and a_(3)x+b_(3)y+c_(3)=0 are concurrent then |{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|=0