Question

A point Q at a distance 3 from the point P(1,1,1) lying on the line joining the points A(0,-1,3) and p has coordinates____

Answer 1

point P=(1,1,1)
point A=(0,-1,3)
distance between P and A = √[(1-0) ²+(1--1)²+(1-3)² ]
= √[1²+2²+(-2)²]
= √[1+4+4]
= √9
=3
since Q is a point at a distance 3 units from P, Q coincides with A.
ie Q=(0,-1,3)
also,the next point lies in an opposite direction from P(diametrically opposite to A when we draw a circle with P as centre and radius 3)
since it lies diametrically opposite to A, P becomes the midpoint of Q and A.
so
1=(x+0)/2
x=2
and
1=(y-1)/2
y=3
also
1=(z+3)/2
z=-1
so the coordinates of 2nd point=(2,3,-1)

So, the cordinates of points at a distance 3 units from P and lies in the line joining P and A =(0,-1,3) &(2,3,-1)