The algebraic sum of perpendicular distances from `A(x_(1),y_(1)), B(x_(2),y_(2))` and `C(x_(3),y_(3))` to a variable line is zero, then all the such lines will always pass thorugh

The algebraic sum of the perpendicular distances from A(x_1, y_1) , B(x_2, y_2) and C(x_3, y_3) to a variable line is zero. Then the line passes through (A) the orthocentre of triangleABC (B) centroid of triangleABC (C) incentre of triangleABC (D) circumcentre of triangleABC

Let the algebraic sum of the perpendicular distance from the points (2, 0), (0,2), and (1, 1) to a variable straight line be zero. Then the line passes through a fixed point whose coordinates are___

If the algebraic sum of the perpendicular distances from the points (3, 1), (-1, 2) and (1, 3) to a variable line be zero, and |(x^2+1, x+1, x+2), (2x+3, 3x+2, x+4), (x+4, 4x+3, 2x+5)|= mx^4 + nx^3 + px^2 + qx+r be an identity in x , then the variable line always passes through the point (A) (-r, m) (B) (-m, r) (C) (r, m) (D) (2r, m)

L is a variable line such that the algebraic sum of the distances of the points (1,1) (2,0) and (0,2) from the line is equal to zero. The line L will always pass through a. (1,1) b. (2,1) c. (1,2) d. none of these

If the algebraic sum of the perpendiculars from the points (2,0),(0,2),(1,1) to a variable line be zero, then prove that line passes through a fixed-point whose coordinates are (1,1)dot

If the lines x=a_(1)y + b_(1), z=c_(1)y +d_(1) and x=a_(2)y +b_(2), z=c_(2)y + d_(2) are perpendicular, then

If A (x_(1), y_(1)), B (x_(2), y_(2)) and C (x_(3), y_(3)) are vertices of an equilateral triangle whose each side is equal to a, then prove that |(x_(1),y_(1),2),(x_(2),y_(2),2),(x_(3),y_(3),2)| is equal to

The variable plane x+3y+z-4+lambda(2x-y)=0 always passes through the line

The algebraic sum of distances of the line ax + by + 2 = 0 from (1,2), (2,1) and (3,5) is zero and the lines bx - ay + 4 = 0 and 3x + 4y + 5=0 cut the coordinate axes at concyclic points. Then (a) a+b=-2/7 (b) area of triangle formed by the line ax+by+2=0 with coordinate axes is 14/5 (c) line ax+by+3=0 always passes through the point (-1,1) (d) max {a,b}=5/7

Find the perpendicular distance of the point (1, 1, 1) from the line (x-2)/(2)=(y+3)/(2)=(z)/(-1) .