Question

The co-ordinates of the points which divides line segment joining the point A(2, –6, 8) and B(–1, 3,–4) internally in the ratio 1: 3' are ______.

Options

• `(5/4, 15/4, 5)`

• `(5/4, (-15)/4, 5)`

• `((-5)/4, (-15)/4, 5)`

• `(5/4, (-15)/4, -5)`

Answer 1

The co-ordinates of the points which divides line segment joining the point A(2, –6, 8) and B(–1, 3,–4) internally in the ratio 1: 3' are `(5/4, (-15)/4, 5)`.

Explanation:

Let `"R"(bar"r")` divide line AB internally in the ratio 1 : 3.

∴ `bar"r" = (bar"b" + 3bar"a")/(1 + 3)`

= `(1(-hat"i" + 3hat"j" - 4hat"k") + 3(2hat"i" - 6hat"j" + 8hat"k"))/4`

= `(5hat"i" - 15hat"j" + 20hat"k")/4`

= `(5hat"i")/4 + ((-15hat"j")/4) + 5hat"k"`

∴ Co-ordinates of R are `(5/4, (-15)/4, 5)`