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.

Given: , and 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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