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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

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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"`.

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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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