# A point P with position vector ijk-14i^+39j^+28k^5 divides the line joining A (1, 6, 5) and B in the ratio 3 : 2, then find the point B. - Mathematics and Statistics

Sum

A point P with position vector (- 14hat"i" + 39hat"j" + 28hat"k")/5 divides the line joining A (1, 6, 5) and B in the ratio 3 : 2, then find the point B.

#### Solution

Let A, B and P have position vectors a, b and p respectively.

Then bar"a" = - hat"i" + 6hat"j" + 5hat"k",

bar"p" = (- 14hat"i" + 39hat"j" + 28hat"k")/5

Now, P divides AB internally in the ratio 3 : 2

∴ bar"p" = (3bar"b" + 2bar"a")/5

∴ 5bar"p" = 3bar"b" + 2bar"a"

∴ 3bar"b" = 5bar"p" - 2bar"a"

∴ 3bar"b" = 5((- 14hat"i" + 39hat"j" + 28hat"k")/5) - 2(- hat"i" + 6hat"j" + 5hat"k")

= - 14hat"i" + 39hat"j" + 28hat"k" + 2hat"i" - 12hat"j" - 10hat"k"

= - 12hat"i" + 27hat"j" + 18hat"k"

∴ bar"b" = - 4hat"i" + 9hat"j" + 6hat"k"

∴ coordinates of B are (-4, 9, 6).

Concept: Vectors and Their Types
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