The position vector of points A and B are ab6a¯+2b¯ and aba¯-3b¯. If the point C divides AB in the ratio 3 : 2, show that the position vector of C is ab3a¯-b¯. - Mathematics and Statistics

Sum

The position vector of points A and B are 6bar"a" + 2bar"b" and bar"a" - 3bar"b". If the point C divides AB in the ratio 3 : 2, show that the position vector of C is 3bar"a" - bar"b".

Solution

Let bar"c" be the position vector of C.

Since C divides AB in the ratio 3 : 2,

bar"c" = (3 (bar"a" - 3bar"b") + 2(6bar"a" + 2bar"b"))/(3 + 2)

= (3bar"a" - 9bar"b" + 12bar"a" + 4bar"b")/5

= 1/5 (15bar"a" - 5bar"b") = 3bar"a" - bar"b"

Hence, the position vector of C is 3bar"a" - bar"b".

Concept: Section Formula
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