Q. 115.0( 1 Vote )
The position vectors of points A, B and C are and respectively. If C divides the lien segment joining A and B in the ratio 3 : 1, find the values of λ and μ.
Let the position vectors of points A, B and C be, and respectively.
C divides AB internally in the ratio 3:1.
Recall the position vector of point P which divides AB, the line joining points A and B with position vectors and respectively, internally in the ratio m : n is
Here, m = 3 and n = 1.
We have, and
By comparing both sides, we get 36 + λ = –44
⇒ λ = –44 – 36
∴ λ = –80
We also have 3μ + 3 = –12
⇒ 3μ = –15
∴ μ = –5
Thus, λ = –80 and μ = –5
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