If P divides the line segment joining the points A(1,2,-1) and B(-1,0,1) externally in the ratio 1: 2 and Q=(1,3,-1) , then P Q=

Step-by-step solution

Given, points A(1,2,-1) and B(-1,0,1) and P divides the line segment externally in the ratio 1: 2 For external division, coordinates are [ m₁ x₂-m₂ x₁ m₁-m₂ , m₁ y₂-m₂ y₁ m₁-m₂ , m₁ z₂-m₂ z₁ m₁-m₂ ] aligned & = [ 1(-1)-2(1) 1-2 , 1(0)-2(2) 1-2 , 1(1)-2(-1) 1-2 ] & = [ -1-2 -1 , -4 -1 , 3 -1 ] & =[3,4,-3] aligned So, P Q= (3-1)^2+(4-3)^2+(-3+1)^2 aligned & = (2)^2+(1)^2+(-2)^2 & = 4+1+4 =3 units aligned