Find the co-ordinates of the centroid of the triangle whose vertices are `(x_(1),y_(1),z_(1)), (x_(2),y_(1),z_(2)) and (x_(3),y_(3),z_(3))`.

The three points (x_(1), y_(1), z_(1)), (x_(2), y_(2), z_(2)), (x_(3), y_(3), z_(3)) are collinear when…………

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

Find the circumstance of the triangle whose vertices are given by the complex numbers z_(1),z_(2) and z_(3) .

Show that the triangle whose vertices are z_(1)z_(2)z_(3)andz_(1)'z_(2)'z_(3)' are directly similar , if |{:(z_(1),z'_(1),1),(z_(2),z'_(2),1),(z_(3),z'_(3),1):}|=0

bb"statement-1" " Let " z_(1),z_(2) " and " z_(3) be htree complex numbers, such that abs(3z_(1)+1)=abs(3z_(2)+1)=abs(3z_(3)+1) " and " 1+z_(1)+z_(2)+z_(3)=0, " then " z_(1),z_(2),z_(3) will represent vertices of an equilateral triangle on the complex plane. bb"statement-2" z_(1),z_(2),z_(3) represent vertices of an triangle, if z_(1)^(2)+z_(2)^(2)+z_(3)^(2)+z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1)=0

Find the vector and cartesian equation of the line passing through the point (2,1,3) and perpendicular to the lines. (x-1)/(1)=(y-2)/(2)=(z-3)/(3) and (x)/(-2)=(y)/(2)=(z)/(5)

Without expanding as far as possible, prove that |{:(1,1,1),(x,y,z),(x^(3),y^(3),z^(3)):}| = (x-y)(y-z)(z-x)(x+y+z) .

Find the distance of the line (x+1)/-3=(y-3)/2=(z-2)/1 in the plane x+y+z+3=0.