Question

Let P = (3, 2, −2) and Q = (7, 9, 9). Find the coordinates of the following. The point on the line through PQ whose distance from P is twice its distance from Q and which does not lie between these two points.

Answer 1

point A ON THE LINE PQ is ( 11,16,20)

Explanation:

GIVEN DATA:

P (3,2, -2)

Q(7,9,9)

SUPPOSE point A has a cordintates (x,y,z)

given that AP = 2AQ

Q is midpoint of AP

So we have
`((x,y,z)+(3,2,-2))/(2) = (7,9,9)`

x+3 = 14.........1

y+2= 18..........2

z-2 =18...........3

x = 11 from equation 1

y = 16 from equation 2

z = 20 from equation 3

Therefore point A ON THE LINE PQ is ( 11,16,20)