Answer: (x1,y1,z1) = (1, 2, 3) (x2,y2,z2) = (-1, -2, -1) (x3,y3,z3) = (2, 3, 2) (x4,y4,z4) = (4, 7, 6) $\begin{array}{l} Length AB =  \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2} + {{({z_2}...

Answer: (x1,y1,z1) = (2, 3, 5) (x2,y2,z2) = (-4, 7, -7) (x3,y3,z3) = (-2, 1, -10) (x4,y4,z4) = (4, -3, 2) $\begin{array}{l} Length PQ =  \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2} +...

Answer: (x1,y1,z1) = (1, 3, 4) (x2,y2,z2) = (-1, 6, 10) (x3,y3,z3) = (-7, 4, 7) (x4,y4,z4) = (-5, 1, 1) $\begin{array}{l} Length PQ =  \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2} + {{({z_2}...

Answer: (x1,y1,z1) = (3, 2, -5) (x2,y2,z2) = (-3, 8, -5) (x3,y3,z3) = (-3, 2, 1) (x4,y4,z4) = (-1, 4, -3) $\begin{array}{l} Length AD =  \sqrt {{{({x_4} - {x_1})}^2} + {{({y_4} - {y_1})}^2} +...

Answer: (x1,y1,z1) = (-2, 3, 5) (x2,y2,z2) = (1, 2, 3) (x3,y3,z3) = (7, 0, -1)   $\begin{array}{l} Length AB =  \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2} + {{({z_2} - {z_1})}^2}} \\...

Answer: (x1,y1,z1) = (3, -5, 1) (x2,y2,z2) = (-1, 0, 8) (x3,y3,z3) = (7, -10, -6)   $\begin{array}{l} Length AB =  \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2} + {{({z_2} - {z_1})}^2}}...

Answer: (x1,y1,z1) = (3, -2, 4) (x2,y2,z2) = (1, 1, 1) (x3,y3,z3) = (-1, 4, -2)   $\begin{array}{l} Length PQ =  \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2} + {{({z_2} - {z_1})}^2}} \\...

Answer: Let us take, C(x,y,z) point equidistant from points A(-1, 2, 3) and B(3, 2, 1). ∴ AC = BC $\sqrt {{{(x + 1)}^2} + {{(y - 2)}^2} + {{(z - 3)}^2}}  = \sqrt {{{(x - 3)}^2} + {{(y - 2)}^2} +...

Answer: Let us take, C(0,y,0) point which lies on y axis and is equidistant from points A(3, 1, 2) and B(5, 5, 2). ∴ AC = BC $\sqrt {{{(0 - 3)}^2} + {{(y - 1)}^2} + {{(0 - 2)}^2}}  = \sqrt {{{(0 -...

Answer: Let us take, C(0,0,z) point which lies on z axis and is equidistant from points A(1, 5, 7) and B(5, 1, -4). ∴ AC = BC $\sqrt {{{(0 - 1)}^2} + {{(0 - 5)}^2} + {{(z - 7)}^2}}  = \sqrt {{{(0 -...

Answer: Let us take, D(x,y,z) point equidistant from points A(a, 0, 0), B(0, b, 0), C(0, 0, c) and O(0, 0, 0). ∴ AD = OD $\sqrt {{{(x - a)}^2} + {{(y - 0)}^2} + {{(z - 0)}^2}}  = \sqrt {{{(x -...

Answer: The general point on yz plane is D(0, y, z). Consider this point is equidistant to the points A(3, 2, -1), B(1, -1, 0) and C(2, 1, 2). ∴ AD = BD $\sqrt {{{(0 - 3)}^2} + {{(y - 2)}^2} + {{(z...

Answer: The general point on xy plane is D(x, y, 0). Consider this point is equidistant to the points A(2, 0, 3), B(0, 3, 2) and C(0, 0, 1). ∴ AD = BD $\sqrt {{{(x - 2)}^2} + {{(y - 0)}^2} + {{(0 -...

Answer: (x1,y1,z1) = (1, 1, 1) (x2,y2,z2) = (-2, 4, 1) (x3,y3,z3) = (1, 5, 5) (x4,y4,z4) = (2, 2, 5) $\begin{array}{l} Length AB =  \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2} + {{({z_2} -...

Answer: (x1,y1,z1) = (0, 1, 2) (x2,y2,z2) = (2, -1, 3) (x3,y3,z3) = (1, -3, 1) $\begin{array}{l} Length AB =  \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2} + {{({z_2} - {z_1})}^2}} \\ =>...

Answer: (x1,y1,z1) = (4, 6, -3) (x2,y2,z2) = (0, 2, 3) (x3,y3,z3) = (-4, -4, -1) $\begin{array}{l} Length AB =  \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2} + {{({z_2} - {z_1})}^2}} \\ =>...

Answer: (x1,y1,z1) = (1, -1, -5) (x2,y2,z2) = (3, 1,3) (x3,y3,z3) = (9, 1, -3) $\begin{array}{l} Length AB =  \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2} + {{({z_2} - {z_1})}^2}} \\ =>...

Answers: (i) R(1, -3, 4) and S(4, -2, -3) (x1,y1,z1) = (1, -3, 4) (x2,y2,z2) = (4, -2, -3) $\begin{array}{l} D = \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2} + {{({z_2} - {z_1})}^2}} \\ D =...

Answers: (i) A(5, 1, 2) and B(4, 6, -1) (x1,y1,z1) = (5, 1, 2) (x2,y2,z2)= (4, 6, -1) $\begin{array}{l} D = \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2} + {{({z_2} - {z_1})}^2}} \\ D = \sqrt...