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
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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