Question

Find the coordinates of the point R which divides the line segment joining the points P (2, -1, -4) and Q (3, -2, 5) externally in the ratio 3 : 2.

Answer 1

x = nx1+mx2/m+n
2×2+3×3/3+2
10/5
x=5

y = ny1+my2/m+n
-2-6/5
-8/6
y = -8/6

z = nz1 + m z2/m+ n
-8+10/5
z=2/5
(x,y,z)= 5, -8/5 , 2/5

Answer 2

Answer:

R = (5 , - 4 , 23)

Step-by-step explanation:

Find the coordinates of the point R which divides the line segment joining the points P (2, -1, -4) and Q (3, -2, 5) externally in the ratio 3 : 2.

if m:n ratio externally

then co-odinates of R

= { (mx₂ - nx₁)/(m-n)  , (my₂ - ny₁)/(m-n)   (mz₂ - nz₁)/(m-n)  }

Point P  x₁ = 2   y₁ = -1  z₁ = -4

Point Q  x₂ = 3   y₂ = -2  z₂ = 5

m = 3  n = 2

Point R

Rx =  (3*3 - 2*2)/(3-2)   = (9-4)/1 = 5

Ry =  (3*(-2) - 2*(-1))/(3-2)   = (-6 +2)/1 = -4

Rx =  (3*5 - 2*(-4))/(3-2)   = (15+8)/1 = 23

R = (5 , - 4 , 23)