Math, asked by rimalnisha123, 1 month ago

the position vector of p and q are 2i+7j and 4i-3j respectively. find the position vector of a point which divides pq externally in the ratio 2:3

Answers

Answered by amitnrw
1

Given : the position vector of p and q are 2i+7j and 4i-3j respectively.

To find  : the position vector of a point which divides pq externally in the ratio 2:3

Solution:

p = 2i+7j    (2 , 7)

q = 4i-3j   ( 4 , - 3)

point r   divides pq externally in the ratio 2:3

Formula for external division m : n

( mx₂  - nx₁) /(m - n)  .  ( my₂  - ny₁) /(m - n)

m = 2  , n = 3

x₂ = 4  , x₁= 2

y₂ = -3   , y₁ = 7

rx =  (  2 * 4 -  3 * 2)/(2 - 3)  =  2/-1  = - 2

ry =  (  2 * (-3) -  3 * 7)/(2 - 3)  =  -27/-1  = 27

( - 2 , 27)

= -2 i  + 27 j

the position vector of a point which divides pq externally in the ratio 2:3

is -2 i  + 27 j

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